Wrexham maintained their fine opening day record in the Conference, but a spirited performance by newly-promoted Welling ensured that it was perhaps their toughest start to a season in the fifth tier.
An 83rd minute winner from Rob Ogleby, who had just been introduced by Andy Morrell, secured the three points, rewarding a commanding second half performance by The Dragons. It was a different story before the break, though, and Wrexham were grateful to Joslain Mayebi for pulling off a string of saves to keep them in the match.
Morrell, who left his sickbed to be present, gave starts to youngsters Bradley Reid and Steve Tomassen but it was The Wings who started more brightly. Fraser Franks, under pressure from Mark Creighton, put a Loui Fazakerley corner wide from close range and Lee Clarke's twenty-five yard rasper was brilliantly tipped round the post by Mayebi before Wrexham took the lead against the run of play.
A Joe Clarke corner was headed across the face of goal by Creighton and although Neil Ashton couldn't make contact, Kevin Thornton kept the ball in and laid it off for Clarke, who thundered a terrific shot into the top left corner from the edge of the area.
For a while Welling looked stunned and Wrexham, with their tails now up, threatened to run away with the game. Tomassen, popping up unexpectedly in the box, headed a good Jay Harris cross wide from fifteen yards and a deflected Andy Bishop save drew a save from Lee Butcher before Welling could regain their composure.
However, to their massive credit, Welling did regain a foothold in the match and went on to dominate the rest of the half. Ross Lafayette planted two close range headers off target and drew a smart save from Mayebi, who pushed a twenty yard strike round the post.
Mayebi also came to the rescue when Clarke was played clear, the Cameroonian stopper standing up well to repel a powerful drive, but he was helpless when what felt like an inevitable Welling equaliser came two minutes before the break. It was a beautifully conceived and executed goal too: Jake Gallagher swept a perfect cross in from the right and Joe Healy met it perfectly with his head, sending the ball in a perfect arc over Mayebi and into the top right corner.
Kurtis Guthrie could have made matters even worse in injury time, but he headed a Healy free kick wide from six yards out. He would rue that missed chance, as Wrexham came out a different team after the break. They imposed themselves from the start, and Thornton had the ball in the net but the flag had rightly gone up as Adrian Cieselwicz's shot after Butcher punched unconvincingly hit an offside team mate.
Cieslewicz went close again soon after with a spectacular opportunistic effort, latching onto a Reid header and somehow hooking a volley on the stretch from a tight angle which went over the keeper and nearly dipped under the bar. Marco Van Basten would have been proud of that one!
Bishop also went close to scoring on his second debut for The Dragons as he headed a Thornton corner against the bar, and Reid headed over after Creighton found himself on the right wing and swept in a good cross, but as the game entered the final ten minutes it looked like The Wings' determined rearguard action would earn them a point.
With eight minutes left the home side were furious not to win a penalty when Tomassen appeared to have been tripped in the box, but a minute later they got the winner. Bishop held the ball up well before finding Reid on the edge of the area. He fed Ogleby for his first involvement in the game, and the Wales Under-21 striker took full advantage, driving a powerful early shot across Butcher and into the back of the net.
Moments later Ogleby looked to have earned a penalty as Bergqvist pulled him down in the area, and with two minutes of added time played it looked like Welling would make that decision appear crucial as Clarke once more found himself one-on-one with Mayebi from a Blaine Hudson through ball. However, Stephen Wright appeared out of nowhere to block Clarke's shot and a relieved Wrexham were soon celebrating a very hard-fought win.
Wrexham (4-3-3): Mayebi; Tomassen, Creighton, Wright, Ashton; Clarke, Harris, Thornton (Evans 86); Reid (Hunt 89), Bishop, Cieslewicz (Ogleby 82).
Subs: Coughlin, Rushton.
Welling United (4-5-1): Butcher; Fazakerley, Hudson, Franks, Blomqvist; Guthrie (Pires 67), Gallagher, Dyer, Clarke, Healy (Jack Obersteller 79); Lafayette.
Subs: Turner, Joe Obersteller, Hughes-Mason.
Referee: Kevin Johnson
Wrexham: Harris (foul), Wright (foul)