Liverpool climbed to the top of the Premier League as Darwin Nunez ended his goal drought to inspire a 2-0 win against Burnley.
Jurgen Klopp's side took an early lead through Nunez at Turf Moor and held on despite wasting a host of chances.
Nunez's eighth goal this season was his first for 12 games since he netted against Bournemouth in the League Cup on November 1.
Diogo Jota, back from a month's injury absence, wrapped up the victory late on to leave Liverpool two points above second placed Arsenal, who have a game in hand.
"We played an incredible game and then it was just 1-0 for so long, which was really strange!" Klopp said.
"Nunez is an incredible finisher but if a striker doesn't score, the whole system is not the same. You question everything."
At Old Trafford, United were in danger of another damaging defeat when goals from John McGinn and Leander Dendoncker put Villa in control by half-time at Old Trafford.
Erik ten Hag's team were booed off at the interval but they staged a much-needed revival, sparked by Alejandro Garnacho scoring their first goal in seven hours and twenty minutes.
Garnacho struck again to equalise before Hojlund finally scored his first Premier League goal, in his 15th appearance, with eight minutes left.
Hojlund's cathartic strike ended United's four-match winless run in all competitions and lifted them to sixth in the Premier League.
"At half-time I said to the team, 'keep believing'. The atmosphere changed a lot from the first half to the second. If we play our best we can beat anyone," Ten Hag said.
Two games without a win have dented Villa's unexpected title challenge.
Unai Emery's men remain third, three points behind Liverpool after their first defeat in 11 matches in all competitions.
Arsenal can regain top spot with a victory at home to West Ham on Thursday.
Elsewhere, Bournemouth were 3-0 winners against Fulham while Luton forced two own goals from Sheffield United late to bag a 3-2 victory. (AFP)