Michy Batshuayi fired wide for the home side before Martial's glancing header from Aaron Wan-Bissaka's cross put United in front on the stroke of half-time.
Chelsea substitute Kurt Zouma had a goal disallowed after a Video Assistant Referee review ruled that Cesar Azpilicueta had fouled Brandon Williams in the build-up.
Bruno Fernandes' free-kick hit the post before his corner was powerfully headed in by Maguire to double Man Utd's lead on 66 minutes.
Chelsea's Olivier Giroud also had a goal overturned by the VAR for offside and fellow substitute Mason Mount hit the post, before Odion Ighalo came close to a debut goal in a late cameo.
United move up to seventh with 38 points.
Chelsea: 22 Feb v Spurs (H)
Man Utd: 23 Feb v Watford (H)