Goals from Michael Tonge and Ade Akinbiyi in an eight minute spell should have guided Neil Warnock's side to a comfortable win but a Steve MacLean penalty 11 minutes from time set up a nailbiting finish.
In a frantic opening period Wednesday were handed a half chance, striker Leon Best scooping the ball over the top before United's Akinbiyi almost found a way through. Rob Kozluk's long throw was headed straight to the United striker, whose instinctive low shot was snatched on the line by Chris Adamson.
United full-back Chris Armstrong blundered minutes later when he failed to control MacLean's low cross, Best picked out Chris Brunt as Armstrong recovered to block his low drive.
Brunt tried his luck with a spectacular strike from 28 yards, Paddy Kenny diving forwards to scoop up the ball before United snatched the lead in spectacular fashion on 37 minutes.
Armstrong was brought down by Brunt on the edge of the area and Tonge drew first blood curling his free-kick into the top right-hand corner from 25 yards.
Paul Ifill saw his 20-yard strike smothered by Adamson before United snatched a second in first-half injury time with Armstrong again involved.
Peter Gilbert failed to clear the United defender's cross from the left and Akinbiyi lashed the ball past Adamson from 15 yards, his second goal since joining United from Burnley in a £1.75million move last month.
Northern Ireland international Brunt had a left-foot strike stopped by Kenny and Gilbert managed to get on the end of Brunt free-kick but pulled the ball wide of the target as Wednesday looked for a way back.
Akinbiyi should have killed off Wednesday on 58 minutes as he connected with Bruce Dyer's inch-perfect cross from the right but he headed over from four yards.
Adamson foiled Kozluk, snapping up his fierce drive, but it was United who always looked the more likely to score.
Dyer missed an open goal laid on by Akinbiyi before Wednesday were back in the game on 79 minutes, MacLean was brought down in the box and stepped forward to send Kenny the wrong way from the spot.
United survived two late penalty appeals and Kozluk cleared a Brunt effort off the line seconds from time as Neil Warnock's side hung on.