Patrick Bamford hit his first league goal for Marcelo Bielsa's side five minutes after coming on as a second-half substitute.
Bamford, a £7 million recruit from Middlesbrough, had not featured for Leeds since August 31 due to a knee injury.
But the 25-year-old striker made up for lost time as he netted the 66th minute strike that gave Leeds a fifth successive league victory and a one-point lead over Norwich in the race for promotion to the Premier League.
"It was hard win but a deserved one. Bamford can be very important. For him, it is very good for his confidence," Bielsa said.
"He has worked very hard to gain his full fitness. It's important to have two good strikers in our team."
Norwich could have reclaimed pole position with a win at Ashton Gate in the day's late game, but the Canaries ended up relieved to take a point.
Marco Stiepermann fired Daniel Farke's side ahead, but Famara Diedhiou and Callum O'Dowda responded either side of half-time.
With just 12 minutes left, Max Aaron's 78th minute header rescued Norwich, who are five points clear of third placed West Bromwich Albion.
Jonathan Kodjia's 84th minute header gave Aston Villa a 2-2 draw against Stoke at Villa Park.
Joe Allen broke the deadlock just two minutes into the second half, but Villa equalised in the 73rd minute through a penalty from on-loan Chelsea forward Tammy Abraham.
Stoke went back in front just five minutes later when Benik Afobe converted from the spot.
Swansea scored two goals in as many second half minutes to beat Sheffield Wednesday 2-1 at the Liberty Stadium.
Birmingham fought back from two goals down to draw 2-2 at Blackburn, while Middlesbrough's play-off push was hit by a 2-1 defeat at QPR.
Hull beat Brentford 2-0 to increase the pressure on Bees boss Thomas Frank, while Preston beat struggling Millwall 3-2 at Deepdale.
Managerless Reading moved out of the bottom three after a 1-1 draw at Rotherham.
Bottom of the table Ipswich finally clinched their first home league win of the season with a 1-0 victory over Wigan thanks to Freddie Sears' 67th minute goal.