Striker Patrick Bamford opened the scoring for the visitors, collecting a pass from midfielder Mateusz Klich and firing in his 15th goal of the season, while midfielder Kalvin Phillips added a second with a curling free kick from 25 yards.
Adam Armstrong pulled one back for Blackburn shortly after the restart before Klich netted United's third goal five minutes later.
Earlier in the day, fifth-placed Nottingham Forest were held 1-1 by Derby County in the East Midlands derby.
Winger Joe Lolley scored the opening goal with a low, skidding effort from outside the box to hand Forest an early lead but Derby's Chris Martin netted an injury-time equaliser as he bundled in captain Wayne Rooney's free-kick.
Derby's Martyn Waghorn was shown a straight red card after a challenge on midfielder Ryan Yates minutes before the equaliser.
Fulham kept their hopes of automatic promotion alive with a 1-0 win over Birmingham City to move up to fourth, thanks to an injury time winner from 23-year-old Josh Onomah.
Brentford sealed their fifth consecutive win and closed the gap on second-placed West Bromwich Albion -- who play Hull City on Sunday -- to two points with a 3-0 win over Wigan Athletic.
Said Benrahma's hat-trick compounded misery for Wigan, who entered administration on Wednesday in the wake of the coronavirus pandemic.
Meanwhile, Yakou Meite scored four goals as bottom-placed Luton Town were thrashed 5-0 by Reading.
Sixth-placed Cardiff City beat Bristol City 1-0 to move within six points of fourth-placed Fulham while Huddersfield Town and Preston North End played out a goalless draw.
Stoke City climbed out of the relegation zone and moved up to 18th with a 4-0 win over struggling Barnsley.
Eighth-placed Millwall beat Charlton Athletic on Friday for their first win since the league's restart on June 20 to remain in contention for a playoff spot.
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