The skipper’s first appearance since March 4 came in place of the injured Zlatan Ibrahimovic – set to miss the rest of the season with a knee ligament injury – as United won comfortably to extend their unbeaten run to 23 league matches.
Anthony Martial gave United the lead with his 25th United goal, completing a terrific counter-attack with a cool finish after swapping passes with Ander Herrera.
And United’s advantage was doubled by Rooney before the interval, the club’s record goalscorer on hand to turn home a loose ball after Tom Heaton could only parry Martial’s effort.
Burnley rarely looked likely to make a comeback and United were able to conserve energy in the second half after their exertions against Anderlecht in the Europa League, though they may have another injury concern to contend with after Paul Pogba limped off late on.
United move a single point behind rivals Manchester City in the race for Champions League qualification ahead of Thursday’s pivotal derby clash at the Etihad Stadium, while Burnley have won only one of their last 11 league matches and remain 15th, five points above the relegation zone.