Leeds United's promotion rivals Sheffield United failed to secure a vital three points against Millwall at Bramall Lane.
The Blades were being held by the Lions at the break but Madine ran onto a John Fleck through-ball and slotted home with 51 minutes on the clock.
On the 85th minute John Egan was sent off for handling the ball on the line but Ben Marshall missed the penalty.
However, Jake Cooper was on hand to deny Sheffield United the win in added time to give Leeds a huge boost ahead of tonight's game against Sheffield Wednesday at Elland Road.
A win for Marcelo Bielsa's charges would see them establish to a two-point gap ahead of Chris Wilder's side.
Elsewhere in the Championship, Aston Villa won the battle of the play-off teams with Tammy Abraham and Conor Hourihane confirming a 2-0 win against Bristol City.
Villa have now won eight matches in a row as Dean Smith's side hit form at the right time.
West Brom all-but ended Preston North End's slim play-off hopes with an impressive 4-1 win at the Hawthorns.
League leaders Norwich City are in action on Sunday as they take on Wigan Athletic at the DW Stadium.
Ipswich Town have been relegated after their 1-1 draw with Birmingham City.
Leeds United make late change to starting XI as Liam Cooper suffers injury in warm-up
Championship results
Derby County 4-0 Bolton Wanderers
Ipswich Town 1-1 Birmingham City
Middlesbrough 1-0 Hull City
Nottingham Forest 1-2 Blackburn Rovers
Queens Park Rangers 4-0 Swansea City
Reading 2-1 Brentford
Sheffield United 1-1 Millwall
Stoke City 2-2 Rotherham United
West Brom 4-1 Preston North End
