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The Red Devils went into their Premier League clash at Turf Moor level on points with defending champions Liverpool.
United skipper Harry Maguire thought he had handed his side the lead in the first half, only for his headed effort to be ruled out without VAR coming into action.
However, United finally broke the deadlock late into the second half through Pogba.
The in-form Bruno Fernandes found Marcus Rashford down the right before the United forward picked out Pogba with a cross.
Pogba connected with a first-time volley and was fortunate to see his effort take a deflection off Matt Lowton's leg and head through the legs of Nick Pope.
United's 1-0 win over Burnley has Ole Gunnar Solskjaer's men top of the table on 36 points, three points ahead of Jurgen Klopp's Liverpool.
Klopp's side can climb back to the top of the Premier League table should they beat United in their showdown at Anfield on Sunday.
Liverpool legend John Aldridge has warned the Reds that United will 'sense their weaknesses' in "trying to hit long balls" and will exploit them.
"They'll back themselves on the break with the pace they've got up front but I don't think the fans would be allowing that," he wrote for the Liverpool Echo.
"I think it'll be a pretty open game and they'll sense our weaknesses in trying to hit long balls between young Rhys Williams or Nat Phillips and Trent Alexander-Arnold.
"That's what teams do, they pinpoint that area because our full-backs get forward and take up advanced positions, so then we struggle.
"The left channel is not too bad, because Fabinho looks up and sees it but for the young lads -- as well as they're doing and they are doing superbly -- it's really hard.
"Teams have a lot of quality and players who can put the ball in difficult areas with people chasing them -- the likes of which Rashford will do."
Featured Image Credit: BT Sport/PA
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