Erik ten Hag's side 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.
United 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 ended his goal drought with eight minutes left.
It was Hojlund's maiden league goal for United in his 15th appearance and his sixth in all competitions since his August move from Atalanta.
Hojlund's cathartic strike ended United's four-match winless run in all competitions and lifted them to sixth in the Premier League.
Two games without a win have dented Villa's unexpected title challenge.
Unai Emery's men remain third, three points behind leaders Liverpool after their first defeat in 11 matches in all competitions.