Patrick Bamford struck 12 minutes from time at Hillsborough on Tuesday to lift Steve McClaren's side above QPR in the table and just two points behind second-placed Burnley.
The result leaves Wednesday - who have now lost two league games on the bounce after a eight-game unbeaten run - in 17th.
Wigan Athletic continued their play-off push with a comfortable 2-0 home win over relegation-threatened Barnsley, with first-half goals from on-loan duo Nicky Maynard and Martyn Waghorn doing the damage.
Tuesday's other game in the Championship saw bottom-placed Yeovil Town hold Watford to a 0-0 draw at Huish Park.
Meanwhile, in League One, Leyton Orient got their promotion challenge back on track with a 2-0 victory over basement club Stevenage at Brisbane Road - that win lifting them above Wolves into second place.
Bradford City ended a 13-game winless streak by beating Port Vale 1-0, and Carlisle United picked up a 2-1 away win at Coventry City.
Meanwhile, MK Dons played out a 0-0 stalemate with Preston North End and Crawley Town's home fixture with Tranmere Rovers was postponed.
In League Two, Oxford United missed the chance to go second by losing 3-2 at play-off contenders Newport County, while Accrington Stanley drew 0-0 at home with Bury.
All three of Tuesday's other fixtures in the fourth tier - Rochdale against Burton Albion, Southend United versus Hartlepool United and Exeter City's home game with Morecambe - finished 1-1.
