Kevin Wilkin`s confident side took the lead 5 minutes before the break when a corner was headed back across goal by Alex Gudger for Lee Ndlovu to nod home.
That was about it until the last 3 minutes of normal time when Moors had James Curtis sent-off for a second bookable offence.
And almost immediately afterwards, sub Matt Lowe slotted home the Saints second.
Harrogate Town and Southport are the only other teams yet to taste defeat in 2017/18.
Harrogate are second in the fledgling table on goal difference after coming out on top of an amazing nine-goal thriller at The Martin & Co Stadium against a Gainsborough Trinity side, for whom this was a fourth loss in five.
The hosts lead twice in the first half through Ashley Worsfold aftere 13 minutes and Bradley Wells right on half-time after Louis Jones’ own goal had squared things on 33 minutes.
Harrogate then went 4-2 up with a brace from Joe Leesley on 54 and 60 minutes after Dom Knowles had made it 2-2 just 4 minutes after the interval.
But Craig King on 70 minutes and Shane Clarke 3 minutes later pulled it back to 4-4.
Then, with 7 minutes of normal time remaining, Terry Kennedy headed in George Thomson’s corner to win for the visitors.
Southport had a much quieter, but nevertheless just as important, 1-0 win at the Impact Arena against Alfreton Town.
The only goal of a hard-fought win for Port came after 57 minutes with a goal worthy of three points from Steven Schumacher, who fired home from 20 yards from Brad Jackson's set-up.
Salford City earned a fourth win in five with a 3-0 Moor Lane success against another fancied side, Kidderminster Harriers.
A hat-trick from half-time substitute Jack Redshaw was the difference between the two sides.
Redshaw netted two in quick succession at the beginning of the second half to put Harriers on the backfoot.
That all came after Salford goalkeeper Max Crocombe had kept out a Joe Ironside penalty on the stroke of half-time.
And the former Morecambe and Blackpool striker Redshaw completed his hat-trick 10 minutes from time.
York City achieved a third win following relegation, beating Nuneaton Town 4-3 at Bootham Crescent.
The Minstermen appeared totally in charge when Michael Rankine, inside the opening minute, and Simon Heslop, courtesy of a brilliant volley after 23 minutes, gave them a 2-0 lead the break.
Heslop then added another 7 minutes into the second period before former City striker Ashley Chambers after 68 minutes and Rankine 2 minutes later rapidly exchanged penalties.
Chambers pulled a second back for Boro on 83 minutes and Jordan Nicholson netted again for the visitors a minute from time as the hosts threatened to throw away three points.
Tamworth`s third win from five came courtesy of a comfortable 4-1 success at The Lamb against Curzon Ashton.
A rare brace from Steph Morley after 17 and 25 minutes gave the hosts a 2-0 interval lead.
Then on 79 minutes, Darryl Knights fired home number three from a right-wing cross by Brandon Fox.
A minute later, Bradley Reid drives through the Curzon defence and slotted home coolly.
Two minutes later, Curzon were reduced to ten-men when Steve Howson brought down Reid on the edge of the box and was shown a straight red card.
But the ten-men managed a consolation goal in stoppage time when Niall Cummins fired home from close range.
North Ferriby United, relegated from the National League at the end of last season, won their first game of the new season.
The Villagers inflicted a second home defeat on newly-promoted Blyth Spartans.
Akeel Francis’ 62nd minute effort from a Joe Pugh’s cross proved to be the decisive moment.
FC United of Manchester fell to the foot of the early-season table after they suffered a 3-0 defeat at the Horsfall Stadium against Bradford Park Avenue – meaning the Reds are the only side in the division yet to find a win.
Avenue opened the scoring in the 17th minute after great work from Oli Johnson, his chipped cross to the back post left Adam Boyes with the simplest of tasks to net his third goal of the season.
Having controlled the first period, it wasn’t until the 55th minute that Bradford extended their lead. Johnson again the creator as he played a brilliant pass through to Wayne Brooksby who finished brilliantly into the bottom corner.
And 10 minutes later Brooksby had his second after Boyes` shot was saved, the winger being on hand to fire in the rebound.
Boston United achieved a second three-point haul of the season to date by beating Chorley 2-0 at the Jakemans Stadium.
Ashley Hemmings opened the scoring after 37 minutes.
And then 2 minutes into the second half, Kabongo Tshimanga found the net as the Pilgrims made it two wins from two at home.
AFC Telford got back to winning ways thanks to a 1-0 victory away at Blackwell Meadows against Darlington FC.
Marcus Dinanga's goal 2 minutes into the second half proved the difference.
Newly-promoted Leamington fell to a fourth defeat in five at the New Windmill Ground against a Stockport County side, for whom this was a second win.
Boosted by a healthy following of visiting fans, 844 saw an amazing comeback by the Hatters, who were trailing 2-1 with 8 minutes of normal time left.
Jason Oswell put Stockport ahead after 16 minutes, but they fell 2-1 behind to goals from Rob Thompson-Brown after 37 minutes and then Liam Canavan on 82 minutes.
But Oswell grabbed his second to reduce the deficit to one 4 minutes later, and then in the 5th minute of time added on, Oswell completed his hat-trick to win if for Jim Gannon`s side.