Pogba struck in the 71st minute after his volley deflected off the outstretched leg of Burnley defender Matt Lowton and wrong-footed the Burnley goalkeeper Nick Pope.
Ole Gunnar Solskjaer’s side moved onto 36 points from their 17 games. They play Liverpool on Sunday at Anfield.
“We had to dig in and earn it against Burnley and we did," said Solskjaer.
"We feel very confident going into games. Away from home we have really done well. We have to believe in ourselves and we do. We've done a great job and it's good times.”
Peak
United last led the Premier League in September 2017 when Jose Mourinho was in charge. However, Manchester City eventually took control of the title race with a run of 18 wins on the trot.
But it is the first time that United have been top of the league after 17 games since December 2012. Sir Alex Ferguson drove the team on to the crown in May 2013 before he retired from management.
On Tuesday night at Turf Moor, Burnley applied some late pressure and claimed they should have had a penalty when the ball appeared to hit the arm of the United skipper Harry Maguire. James Tarkowski also squandered a good chance for the hosts.
”It's going to be a test against the champions who have been fantastic,” added Solskjaer. “They've had an unbelievable three seasons but we're ready and we're excited. We’re in a good position going into it.”
