Wednesday twice took the lead, courtesy of Lewis McGugan and Will Keane, only to be pegged back on each occasion by Jake Buxton.
Visiting goalkeeper Keiren Westwood was then sent off with 15 minutes remaining for bringing down Tom Ince and Bent converted the resulting spot-kick to register his fourth goal in as many matches.
That ensured Derby overhauled previous league leaders Middlesbrough, who suffered a first home league defeat since August when going down 1-0 to Leeds United in the day's early kick-off.
A third-minute strike from Alex Mowatt proved decisive for Leeds, who held firm thereafter in the face of Middlesbrough pressure.
Bournemouth were also beaten on Saturday, going down 3-1 to play-off chasing Brentford, who showed little sign of being affected by the news of Mark Warburton's impending departure at the end of the season.
Elsewhere at the top, Norwich City leapfrogged play-off rivals Watford into fifth with a 3-0 win at Vicarage Road, while Ipswich Town lost 1-0 at home to Reading.
At the bottom, Chris Hughton's Brighton and Hove Albion eased their relegation fears by earning a thrilling 4-3 win over their manager's former side, Birmingham City.
Inigo Calderon and Joao Teixeira each scored twice for Brighton, who now sit three points above the relegation zone and level with Rotherham United, who were thumped 5-0 by Wolves at Molineux.
Blackpool remain rooted to the bottom of the table, despite Grant Hall's equaliser earning a 1-1 draw away to Lancashire rivals Blackburn Rovers.
Nottingham Forest thumped 10-man Bolton Wanderers 4-1 to continue their unbeaten start to life under Dougie Freedman, while the games at Millwall and Huddersfield, who faced Fulham and Cardiff City respectively, both ended goalless.
