Anthony Martial scored his 25th goal for United after a devastating counter-attack 21 minutes in to give the visitors the lead, before the returning Rooney – making his first start since early March – bundled the ball home six minutes before the break to make it two.
United’s tempo dropped after the interval but they were rarely troubled by a Burnley side who have won just once in 11 league games, and are now just five points clear of the bottom three.
The result means that is now 23 games unbeaten in the league for United, who move to within a point of Manchester City in fourth ahead of Thursday’s Manchester derby, live on Sky Sports.
Rooney was back in the starting line-up for United, as was Martial, who replaced the injured Zlatan Ibrahimovic as the central striker, but they were bystanders in the early stages as Burnley did all the early pressing, Robbie Brady going close with a volley.
Nine minutes in, Rooney was given the chance to get his return to the side off to a flier after Martial had fed Ander Herrera and the Spaniard had poked the ball into Rooney’s feet, but though the United skipper swivelled and flicked for goal, Ben Mee did brilliantly to half-block, making Tom Heaton’s save more comfortable.
Rooney then looped a cross-shot onto the roof of the Burnley net as United countered at will, but the Clarets remained a threat themselves with some direct play.
It wasn’t long before a United counter paid dividends, however, as Martial opened the scoring. The France international carried the ball clear after a Burnley corner and laid it off to Herrera, before collecting the return pass and slotting home – a goal that is now set to trigger an £8.5m bonus payment to Monaco.
Burnley responded well, and put plenty of crosses into the United box, but Mourinho’s men stood firm, and six minutes before the break, they were two goals to the good.
Pogba did brilliantly to keep the move alive, dragging the ball away from the defender before nudging it through for Martial, who was denied by Heaton, the ball rebounded to Rooney, who just sneaked the ball over the line.
After the break, Burnley really struggled to find any fluidity, and Pogba almost made them pay for their sloppy play, as he picked up the loose ball, before rifling an effort at goal, but Heaton got two strong hands to the ball to beat it away.
The game petered out as the half wore on, with Michael Keane going closest to getting his Burnley side back in the match late on, but he headed wide after getting up highest to meet a free-kick.
Substitute Marcus Rashford and Pogba again almost netted a third late on, but were both denied by the fingertips of Heaton as United saw the game out with relative ease.
