United scored once in either halves to dish out a grinding victory.
Chelsea saw two goals get overruled by VAR.
Meanwhile, there was another contentious decision regarding Harry Maguire.
Here we present the report and the records broken.
How VAR went on to aggrieve Chelsea at the Bridge?
Maguire was fortunate to escape a red card for kicking Michy Batshuayi in the groin as they tangled on the touchline.
VAR denied Chelsea again when Kurt Zouma had made it 1-1.
The goal was ruled out for a push by Cesar Azpilicueta.
Replays showed Fred put a hand on the back of Azpilicueta.
Lastly, Olivier Giroud's 76th-minute header was ruled out for off-side.
How did the match pan out?
French forward Anthony Martial glanced in Aaron Wan-Bissaka's cross on the stroke of half-time to hand United a 1-0 lead. United captain Maguire powered in a header from Bruno Fernandes' corner after 66 minutes. Both sides had one shot hit the bar from free-kicks.
United complete league double over Chelsea, script record
Manchester United managed to complete their first league double over Chelsea since 1987/88.
This was also the first time United completed a league double over Chelsea without conceding a goal since 1964-65.
United beat Chelsea for the third time across competitions this season.
They also overcame Chelsea twice at the Bridge this season.