The skipper's first start 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.
Robbie Brady had the game's first sight of goal after five minutes when Michael Keane flicked on a free-kick, but the winger's volley flashed over the crossbar.
Rooney's deflected shot from Herrera's cutback was claimed by Heaton and Marouane Fellaini headed straight at the former United goalkeeper as a high-tempo start continued at a sunny Turf Moor.
And United made the breakthrough after 20 minutes with a brilliantly rapid counter-attacking goal.
6 - Ander Herrera has provided six assists in the Premier League this term, as many as in his previous two campaigns combined. Inspired.— OptaJoe (@OptaJoe) April 23, 2017
Brady's cross was cut out and Martial burst away from Joey Barton before playing a neat one-two with Herrera and slotting home from close range.
Ashley Barnes and Ben Mee narrowly failed to convert terrific Brady crosses and a ruthless United took full advantage by extending their lead after 38 minutes.
Pogba slipped Martial through the left channel and, although Heaton saved the Frenchman's shot, Rooney responded to poke home the rebound from close range for his 251st United goal.
United continued to threaten after the interval and Pogba forced a good save from Heaton with a deflected long-range drive, but Jose Mourinho's men appeared happy with a two-goal lead.
Burnley failed to record a single shot on target as the visitors controlled a quiet second period comfortably, with Eric Bailly magnificent in defence, and United's long unbeaten run continues to boost their Champions League hopes.
But United will rue too many dropped points at Old Trafford - having endured 10 draws in that run - as no team has ever gone so long without defeat in a Premier League season and not gone on to claim the title.
KEY OPTA STATS
- Burnley failed to land a shot on target in a Premier League home game for only the second time in their history (also vs Liverpool in December 2014).
- Man Utd have conceded fewer Premier League goals in 2017 than any other team, shipping just five in total.
- Only Alan Shearer (190) has scored in more different Premier League games than Wayne Rooney (149 – level with Frank Lampard & Andrew Cole).
- Anthony Martial has both scored and assisted in a Premier League away game for the first time in his career.
- Herrera is the first Man Utd player to provide an assist in three consecutive Premier League appearances since Juan Mata in February 2014.