Manager Sean Dyche named an unchanged side for the clash at Elland Road from the team which faced Manchester United.
However, notable inclusions were on the bench, including Cornet and Jay Rodriguez, the pair both missed the game at Old Trafford. Kevin Long also returned for the Clarets.
Leeds, who named Raphinha and Diego Llorente in their starting line-up, were backed by a loud crowd in Yorkshire, but the travelling support from Burnley could be heard loud and proud.
Burnley were on the front foot in the opening 15 minutes, and when Leeds moved the ball forward, the away team’s backline stood strong, with Wayne Hennessey making the first stop from Stuart Dallas’ curling right footed shot, 15 yards out.
Raphinha nearly caught Hennessey off guard from 40 plus yards with an ambitious chip but the ball just went over the bar as the home side’s momentum started to grow.
A scramble in the penalty box followed in the 21st minute, with the hosts having two chances to tap home, but a Burnley shirt managed to prod the ball to safety.
The Clarets missed a glorious chance to take the lead just after the half hour mark, when former Leeds duo Charlie Taylor and Chris Wood combined, the former crossing to the latter, and our number nine was denied from close range by Illan Meslier.
Moments later, Tyler Roberts was unmarked and headed wide of Hennessey’s left hand post after a quick breakaway.
Leeds took the lead with five minutes of the first half remaining, as Burnley gave the ball away inside their own half, and Harrison slotted home after his first shot was saved.
The first half concluded with Wood firing over from another Taylor cross, with the Clarets work to do in the second half to find a way back into their first match of 2022.
Sean Dyche introduced Maxwel Cornet for the second half, Johan Berg Gudmundsson the man to make way for the Ivory Coast international.
Leeds squandered a fantastic chance to add to their lead, when Roberts was left in space on the edge of the box, but he fired over. At the other end, Cornet was looking lively for the Clarets, as they looked for a way back into the match at Elland Road.
Cornet won a free-kick on the edge of the box, with Leeds defender Diego Llorente booked. The man himself stepped up and curled the ball into the right hand corner from 25-yards, a stunning free-kick.
Burnley could have snatched a second when Westwood’s corner was low and nearly
tapped home by Cornet.
Leeds could and should have regained the lead when Dan James’ cross went across the goal mouth and into the feet of Raphinha, but with the goal gaping, he hit the side netting.
A beautiful passage of play from the Clarets from their own penalty box nearly led to a goal, as Matt Lowton’s cross was just too far in front of the run of Cornet at the back post.
Leeds regained the lead with 14 minutes remaining, as a shot from outside the penalty area from Dallas flew past a number of blue shirts and Hennessey in the Burnley goal. Burnley brought on Rodriguez for former Leeds man Lennon, with just over ten minutes remaining.
Burnley’s third change saw Matej Vydra come on for Wood as Burnley searched for a second equaliser of the afternoon, but unfortunately it was Leeds who scored the decisive fourth goal courtesy of James’ header in stoppage time.
Burnley: Hennessey, Taylor, Tarkowski, Mee, Lowton, Gudmundsson (Cornet 46), Cork, Westwood, McNeil, Lennon (Rodriguez 79), Wood. Unused subs: Norris, Bardsley, Long, Stephens, Collins, Pieters, Vydra.