It is debatable whether the Dubliner - who netted for the Owls in the last Steel City derby almost three years ago - should be credited with what turned out to be the winner.
However, there was little doubt the Blades were worth the three points as they thanked their manager for snubbing a move to Premiership Portsmouth with a Steel City derby win, reigniting their promotion charge.
Warnock was not so charitable in his selection, changing half his outfield line-up from last week's 4-2 defeat at Leicester.
Craig Short made his first start since mid-September and Rob Kozluk his first appearance since October, while David Unsworth, Neil Shipperley and top scorer Steve Kabba stepped up from the bench in an attacking 4-3-3 formation.
It was the first taste of a Sheffield derby for Paul Sturrock and his entire squad, and the Owls boss handed a debut to his latest loanee Peter Gilbert, with Richard Wood replacing Drissa Diallo.
As expected, there was fierce start to the game, both sides stating their intent with crunching tackles in midfield.
But United soon exposed Wednesday's defensive frailty and would have scored but for a simply unbelievable miss by Kabba.
Danny Webber squared the ball and, from no more than three yards, Kabba scuffed his shot straight at the legs of Nicky Weaver.
The striker was then clean through moments later, but was spared being credited another bad miss by the assistant's flag.
United continued to dominate but were lacking the final ball until the best move of the half saw them take a 24th-minute lead.
Phil Jagielka, Kabba and Webber combined down the right side, the ball eventually reaching Quinn, whose left-foot effort seemed to strike Shipperley on the line before going in.
Quinn, who spent six-and-a-half years at Hillsborough before defecting at the start of last season, then forced a fine stop from Weaver with a dipping free-kick.
The visitors' only attempts of the half had been a weak David Graham strike from 30 yards and an equally unthreatening Daryl Murphy header from an inswinging free-kick, until Craig Rocastle fired inches wide with Paddy Kenny rooted to the spot.
Wednesday began the second half with far more purpose but an attack among the poorest in the Championship was proving little threat to the division's best home defence.
But they at least looked more secure at the back, with United also unable to fashion a worthwhile goal attempt.
They eventually resorted to trying to win a penalty, Kozluk going down far too easily under a challenge from Rocastle.
Murphy came close to playing in substitute Burton O'Brien as Wednesday's confidence grew, while Webber was thwarted by a last-ditch Wood interception at the other end.
The first genuine chance of the half fell to Shipperley, who headed over after a bout of head tennis in the penalty area, although Wednesday were unlucky not to draw level when O'Brien's fine drive arrowed agonisingly wide.
Without a win in their last three games, United's 1-0 lead looked far from secure and Wednesday even saw a goal disallowed for pushing in the box in a nervy final 15 minutes for the hosts.
But the visitors' only effort on target was a Chris Brunt free-kick, their impotence in attack handing United the all-important bragging rights.