The home side started the game with real purpose with Glenn Walker and Adam Walker in particular both causing early problems.
But, just as Boro were starting to see more of the ball, they fell behind on 11 minutes when Ellis Myles found the net from distance with a sweet strike that gave Dean Lyness no chance.
A header from skipper Ryan Beswick was the closest Nuneaton came to spoiling the Saints 100% start.
Newly-pormoted Spennymoor Town also maintained their 100 per cent start, albeit from only three matches, as they eased to a 3-0 Brewery Field win over Bradford Park Avenue.
A quickfire brace from Glen Taylor in the 36th and 38th minutes killed Avenue off.
And when Andy Johnson added a third goal just a minute later, visiting fans feared the worst.
But they managed to stem the flow and the game ended 3-0.
Harrogate Town, Darlington FC and Southport join Brackley and Spennymoor in yet to taste defeat.
Harrogate won 4-1 against Chorley at The CNG Stadium.
Simon Ainge’s first half brace set the foundations against last season’s beaten play-off finalists as Town’s top scorer converted a penalty 3 minutes in, and headed in a second 2 minutes before the break.
Chorley looked a different side after the break, and looked set to mount a comeback when Marcus Carver’s close-range finish halved Town’s lead.
Just as the visitors were growing in confidence, Jordan Thewlis produced a brilliant individual effort to knock the wind out of the Magpies’ sails and send Town on the way to victory.
Scott Leather saw red for the visitors for two bookable offences with just under 15 minutes to go, before Thewlis added his second finishing off Joe Leesley's pull back in the 90th minute.
Darlington`s 100% record went as they shared a 0-0 draw with York City at Bootham Crescent.
Both sides were denied through the woodwork in an entertaining but encounter, despite the lack of goals.
Southport also had to be content with point as they too dropped points for the first time after a 3-3 thriller at the Merseyrail Community Stadium against an FC United of Manchester side for whom this was a first point of the new campaign.
But what this showed is that Port have a lot of fighting spirit as they found themselves 3-1 down with less than 3 minutes left to play before battling back.
James Hooper gave the Reds an early 8th minute lead that Nathan Lowe doubled after 33 minutes.
Liam Martin pulled Port back into the game just past the hour-mark, only for Craig Lindfield to make it 3-1 to the visitors in the 72nd minute.
Adam Dugdale started the comeback with a second in the 87th minute and then Jack Sampson grabbed the equaliser in stoppage time.
Salford City recorded a first ever victory over neighbours Stockport County as well as what was probably their biggest ever crowd at Moor Lane.
A crowd of 2,358 saw the Ammies race into an early 5th minute lead.
And Anthony Dudley put the home side further ahead after 26 minutes.
Connor Hampson gave the large travelling support something to cheer with a response 4 minutes before the break.
However, they weren`t able to find a leveller
Ten-man Boston United were edged out by Tamworth at the Lamb Ground.
Jack Cowgill was red-carded in the incident which saw Reece Styche open the scoring from the spot with less than a quarter of the contest played.
Kabongo Tshimanga equalised 2 minutes after half-time but Darryl Knights won it for the hosts with a spectacular strike in the 71st minute.
Joe Ironside struck a penalty to help secure a 2-0 win for Kidderminster Harriers over newly-promoted Leamington at Aggborough.
Ironside netted for the first time this season in the 64th minute, a goal that proved decisive, a spectacular Emmanuel Sonupe effort in stoppage time finishing things off.
Another newly-promoted side, Blyth Spartans, earned a second win at the higher level with a 4-2 success at the Northolme against Gainsborough Trinity.
Dale Hopson put the visitors in front after just 8 minutes.
And Nathan Buddle doubled that lead 8 minutes later.
Michael Jacklin reduced the arrears on the half-hour mark, only for Sean Reid to restore Blyth`s two-goal cushion with 64 minutes gone on the clock.
Bradley Wells quickly pulled a second back for Trinity, but Dan Maguire added Spartans` fourth with 4 minutes remaining.
North Ferriby United produced their best performance of the season but a 1-0 defeat at the Impact Arena against Alfreton Town still leaves them goalless and pointless at the foot the table.
The Villagers fell behind after 70 minutes. Adam Smith floated a free-kick into the six-yard box and with the Ferriby defence static, Billy Priestley headed home unmarked.