The hosts were 2-0 up by half-time after striker Tammy Abraham struck twice for his third and fourth goals of the season.
But the Blades pulled one back in the first minute of the second half when Callum Robinson, who had missed from close range in the first half, scored his first since joining the club in the summer.
And they pulled level after 89 minutes when Robinson’s cross towards substitute Lys Mousset was diverted into his own net by the unlucky Zouma to leave Frank Lampard still searching for a first home win since he became Chelsea manager.
Chelsea struggled to threaten after United keeper Dean Henderson made a brilliant save in the second half to deny Abraham a hat-trick.
The result puts the visitors, who finished second in the Championship last season, into eighth in the Premier League table, one place above Chelsea.