Former Wrexham keeper Kevin Dearden turned it on against his old club as Torquay made it seven points from three games.
Dearden could do nothing with Andy Morell's 14 minute penalty as Wrexham built on a lively start and they looked as if they might go on to an easy win at that stage.
But six minutes later Kevin Hill equalised with an opportunist header. Andy Dibble parried Lee Canoville' s 20-yarder and Hill finished with a diving header.
And in the 29th minute former Rangers startlet David Graham scored what turned out to be the winner.
He raced away on to a precision pass by Jason Fowler, rounded Dibble and scored from a narrow angle.
Dearden, released by Wrexham 18 months ago produced a brilliant reaction save from Carlos Edwards in the 41st minute, just after substitute Dan Bennett hit the post.
And in the closing stages, as Wrexham threw everything at Torquay in a desperate attempt to salvage a point, Dearden was outstanding.
He produced a series of smart saves, but his handling and positional play were even more important in snuffing out Wrexham's hopes.
In fact, it might have been even worse for the Welsh side.
In the 61st minute Torquay winger Tony Bedeau missed an open goal after a brilliant run which took him passed Dibble and nine minutes later Graham had a penalty saved by Dibble.
Torquay boss Leroy Rosenior said: "I thought the lads looked emotionally and physically drained in the first 20 minutes, after the win at Exeter on Monday.
"But after that I was delighted with the way we got stuck in and we deserved the victory.
"There was nothing tactical that we could do when Wrexham came at us near the end, except working hard, chasing the ball down and getting our tackles in, and they did it."
Wrexham manager Denis Smith said: "We started very well, there weren't a lot of plusses after that.
"We lost Steve Roberts with a back injury early on, and I never realised he was such a good player, we missed him that much.
"I'm not very pleased. Without denigrating Torquay, this is a place where you shouldn't come and get beat.
"We tried something different in the second half with three up front but we weren't as fluent."