Wednesday, who have not won at Bramall Lane since 1967, were overrun by their old rivals, but Neil Warnock's promotion chasers couldn't turn their advantage into goals.
United, surprisingly beaten 4-2 at Leicester last week, should have snatched the lead with just four minutes gone, Danny Webber crossing to Steven Kabba who miscued from six yards, the ball hitting centre-back Graham Coughlan.
Quinn, one of two ex-Wednesday players in the side, reacted quickly after Richie Partridge blundered, whipping in a low cross scooped up by Nicky Weaver with Webber waiting to pounce.
United, in total control finally broke the deadlock after Webber cleverly picked out Kabba on the right flank, the little striker pumped in a low cross which was only half cleared and Quinn steamed in to fire a low drive from 15 yards, the ball hitting Neil Shipperley who was behind the line.
Wednesday's first threat on goal came on 36 minutes after David Unsworth had picked up a booking for a challenge on Partridge. The little winger's free-kick found on-loan Sunderland striker Daryl Murphy, who pulled his stooping header wide of the far post.
Murphy almost snatched an equaliser minutes later as he worked his way across the United area, evading three defender before slamming his right-foot shot a fraction wide of the target.
Weaver pounced to hang on to a Quinn cross and Webber had a fierce shot blocked by Richard Wood after he turned cleverly in the area.
Shipperley missed a chance on 69 minutes, heading over after full-back Rob Kozluk had pumped a Quinn cross into the goalmouth, before Wednesday substitute Burton O' Brien went close with a left-foot shot from 20 yards.
Chris Brunt almost snatched a dramatic equaliser in the dying minutes, his long-range strike smothered on the line by Paddy Kenny.