Oxford went into the tie occupying second-bottom spot in the National League South and have gone eleven league games without a win.
However, at the home (albeit a different one) of one of the FA Cup`s most famous giantkillers, Colchester, who famously knocked out the then mighty Leeds United back in 1971, City triumphed 1-0 with a terrific battling performance.
After a fairly even but goalless opening 45 minutes, City shocked the home side by taking the lead within seconds of the restart when Matty Paterson headed home Dave Pearce`s cross.
Another tremendous performance came from National League side Boreham Wood, who beat another fames cup side, League One Blackpool, at Meadow Park.
The BBC chose Boreham Wood to screen their live lunchtime `Football Focus` programme from and the 1953 FA Cup winners in that infamous `Matthews` final found themselves ousted from this season`s competition at the first attempt.
The Seasiders could certainly have no gripe about the state of the Meadow Park pitch, which was superb as usual, and they had the better of a first half of few clear-cut chances.
And when Blackpool took the lead just past the hour-mark when Danny Philliskirk got on the end of Nathan Delfouneso`s through ball to beat Grant Smith in the home goal, a shock didn`t look on.
However, Luke Garrard`s side were back on level terms within 6 minutes when sub Blair Turgott – one of Jamie Vardy`s V9 Academy graduates – scored from Kane Smith`s cross.
It looked as though Wood were facing a long midweek trek to the north-west seaside for a replay, until 2 minutes from the end of normal time when another sub, Dan Holman, popped up to net the winner for one of the day`s biggest upsets.
Boreham Wood`s league rivals Maidstone United also caused a major upset by going to League Two Cheltenham Town and winning 4-2.
In a fiercely-fought cup tie in which both sides ended up with ten-men, the Stones took a 20th minute lead, thanks to a Delano Sam-Yorke header.
And almost straight from the restart, Joe Pigott poked in a second from close range.
The home side had a mountain to climb when they conceded a third just before half-time when Zavon Hines scored for the Stones to loud boos from the home support.
The experienced Gary Johnson`s side had to come out fighting, and they did just that, reducing the deficit within 7 minutes with a Kevin Dawson header.
But seconds after that, Sam-Yorke made it 4-2 for the visitors and it was back to square one for the Robins.
But his day turned sour 4 minutes later when he was sent-off for a rash challenge on Mohamed Eisa.
An Alex Finney own goal pulled a second back for the home side just past the hour-mark, but any hope Cheltenham had of mounting a comeback were dashed when Dawson was also sent for an early shower after a bad challenge on Maidstone keeper Lee Worgan.
Another National League side, Tranmere Rovers, will fancy their chances of completing an upset after holding League One Peterborough United to a 1-1 draw at London Road.
After a dull first half in which Tranmere had slightly the better of it, it was Posh who broke the deadlock 7 minutes after the break.
Jack Marriott turned the ball in after a corner had been headed down by Ryan Tafazolli.
Rovers` sub Andy Cook – on the field for less than 4 minutes – earned his side a replay when he converted former Posh midfielder Jeff Hughes` cross in the 72nd minute.
Also in the hat for the Second Round draw are Tranmere`s league rivals AFC Fylde, who beat National League North side Kidderminster Harriers 4-2 at Mill Farm.
Danny Rowe gave the Coasters a 14th minute lead when he found the net from 12 yards after turning neatly past a Kiddy defender.
That was the only goal of the opening half, but less than 3 minutes into the second, Fylde were two-up with the prolific Rowe`s second from close range.
Then on 54 minutes the tie looked to be put to bed when a terrific individual effort from Jonny Smith made it 3-0 to the home side.
It became 4-0 just 10 minutes later when Sam Finlay netted after a swift counter-attack.
Harriers battled on though and managed to pull two back through Joel Taylor after 74 minutes and then Andre Brown in stoppage time.
Another National League side in the hat for the next round are Gateshead, who saw off National League South outfit Chelmsford City 2-0 at the International Stadium.
City gave as good as they got early on, but it was the home side who drew first blood on the half-hour mark when Jordan Burrow headed in Wes York`s cross.
And then 4 minutes later, Danny Johnson added a second for the Heed when he curled a lovely effort past Sam Beasant from the edge of the box.
Chelmsford had a couple of decent efforts in the second half, with Gateshead `keeper James Montgomery called into action to prevent Tom Hitchcock and Shaun Batt from reducing the arrears.
It`s the end of the FA Cup road though for Aldershot Town, Bromley, Hartlepool United, Leyton Orient, Macclesfield Town, Ebbsfleet United, AFC Telford United and Gainsborough Trinity, who were both `giantkilled` themselves.
The Bucks were beaten 1-0 at Edgar Street by Evo-Stik League South Premier side Hereford FC, whose former incarnates, of course, caused one of the most famous cup upsets of all time.
In front of a record crowd under the new regime of 4,700, the National League North side were under the cosh after Jonathan Royle was shown a straight red card on the hour-mark for a reckless challenge on Pablo Haysham.
And 8 minutes later, the prolific John Mills pounced to score the only goal when he latched onto a loose ball after Telford `keeper Jasbir Singh had parried Haysham`s initial shot.
Gainsborough were on the end of a thorough hammering at their own Martin & Co Arena by Hereford`s league rivals Slough Town.
The impressive Rebels, sitting second in their division at present, were too strong on the day for a Trinity side who were undone by a second half blitz.
Matt Lench`s 35th minute goal for the visitors was all that separated the team`s at the break.
But within seconds of the restart, Lench doubled his and Slough`s lead and Chris Flood made it 3-0 just 5 minutes later.
Manny Williams made it 4-0 after 71 minutes and the nap hand was completed by sub Sean Fraser 15 minutes from time before Lench clinched the match ball with his third and the Rebels` sixth in the 84th minute.
And it could even had been worse for Trinity as Gavin James missed a stoppage time penalty!
National League side Aldershot Town found League One leaders Shrewsbury Town, managed by former Grimsby Town boss Paul Hurst, too hot to handle and were beaten 5-0.
Ex-Shots man Alex Rodman after 20 minutes and Shaun Whalley from the spot 4 minutes later gave the Shrews a two-goal interval advantage.
And then three goals in 6 minutes shortly after the hour-mark killed the tie off.
Stefan Payne started the spree off and then subs Arthur Gnahoua and Carlton Morris completed it.
The Shots`s National League rivals Bromley, Hartlepool, Leyton Orient, Macclesfield and Ebbsfleet also fell at the First Round stage, with the latter suffering a 6-2 Stonebridge Road battering by League One Doncaster Rovers.
The final outcome didn’t look likely as Fleet led 2-0 with goals from Danny Kedwell from the spot after 35 minutes and Luke Coulson 2 minutes later.
Crucially, however, Rovers scored two goals in injury-time at the end of the first half when Tommy Rowe poked the ball beyond Nathan Ashmore before John Marquis pounced from close-range after Rodney Kongolo's shot had been pushed into his path.
But the visitors took the lead on 52 minutes when James Coppinger's shot took a wicked deflection to beat Ashmore.
Jordan Houghton forced the ball home from close range to make it 4-2 on 78 minutes and it got worse for the hosts when Chris Bush was sent-off 10 minutes from time after picking up a second booking.
Doncaster rubbed salt into the wounds when Coppinger made it 5-2 from the spot and Rowe doubled his own tally to make it 6-2
There was still time for Rowe to double his tally 5 minutes from time.
Another League One side, Rochdale, proved too much for Bromley at Spotland, with the Lancastrians running out 4-0 winners.
Brad Inman after 10 minutes and an Ian Henderson spot-kick just past theb half-hour mark had the home side in control.
Eight minutes into the second half, Inman made it 3-0 with a route-one effort from a long kick from `keeper Josh Lillis and Bromley were reduced to ten-men 15 minutes from time when they had striker Brett Williams dismissed for an alleged stamping offence.
Henderson wrapped up the tie with Dale`s fourth 5 minutes from the end.
Hartlepool travelled across to Morecambe hopeful of causing an upset as Jim Bentley`s side are struggling in League Two.
But Craig Harrison saw the manager of the month award jinx work yet again as the Shrimps won 3-0.
The home side had already forced Pools` keeper Scott Loach into a couple of saves before veteran Kevin Ellison gave the hosts an early 4th minute lead.
Jon Franks came close to equalising early in the second period, but the home side sailed through with goals from Andy Fleming after 67 minutes and a goal accredited to Loach as a shot from Adam Campbell hit a post and then rebounded in off the unfortunate custodian.
Leyton Orient, like Hartlepool, unused to being First Round underdogs, battled hard but were just shaded by League One strugglers Gillingham at the Priestfield Stadium.
A Josh Parker header gave the Gills a 20th minute settler, and that was the half-time score.
The O`s eventually conceded a second in the 75th minute when Tom Eaves forced his way through to beat Charlie Grainger.
James Dayton gave the O`s hope when his free-kick reduced the arrears 4 minutes later.
But they weren’t able to find a leveller and finished with ten-men when Joe Widdowson received a second yellow card in stoppage time.
Macclesfield will be frustrated to have not been able to at least take former rivals and now League Two Forest Green Rovers back to Moss Rose for a replay.
The Silkmen, flying high in the National League, were finally beaten by a 42nd minute Christian Doidge effort from close range after a Scott Laird cross.