Most Gulls fans had given up the ghost when Cheltenham inflicted a second successive home defeat last weekend, but wins at Macclesfield and now this vital victory over play-off outsiders Wrexham have hauled United off the bottom of the table.
It's more than justified chairman Mike Bateson's last-ditch decision to appoint renowned trouble-shooter Ian Atkins as manager with only six games to go.
Now Torquay face a real six-pointer against Stockport at Plainmoor on Tuesday night.
Martin Phillips' early goal was enough to earn all three points against Wrexham, but Torquay lived on their jangling nerves for most of the first half and all of the second.
Winger Phillips popped up in the penalty area to latch onto a loose ball and fired home a 12-yard left-foot shot in the ninth minute.
That goal came after a flying start by Torquay, with Jo Kuffour, Phillips and Steve Woods, with a 55-yard free-kick which just scraped the bar, all going close before Phillips scored. But that was as good as it got for the home side.
Only a brilliant goal line clearance by Woods from in-form striker Matt Derbyshire stopped Wrexham equalising before half-time.
Woods, fellow centre-back Craig Taylor and former Wrexham goalkeeper Andy Marriott were all outstanding as Torquay were forced to soak up relentless second-half pressure.
Marriott saved full-length from the hard-working Jon Walters in the 56th minute, just beat Derbyshire to a Walters' flick 15 minutes later and saw Darren Ferguson slice a great chance over when Walters nodded down a cross from lively substitute Matt Done.
Even in stoppage time Walters might have grabbed an equaliser, but he volleyed just over at the far post when he should have hit the target.
A goal then might not have been enough to keep Wrexham in the play-off hunt, but it would almost certainly have ended Torquay's hopes of staying up.