The forward, who supported the Blues as a boy, calmly slotted the ball home early in the second half after capitalising on Jorginho's error.
But Jorginho made amends for being dispossessed in the lead-up to the goal as he slotted in a penalty after Thiago Silva was booted in the box by Aaron Wan-Bissaka.
Chelsea created far more opportunities in the pulsating Stamford Bridge contest with Callum Hudson-Odoi having an early effort saved by David de Gea, while Antonio Rudiger's long-range effort crashed against the crossbar.
Timo Werner's goalbound effort was blocked by Wan-Bissaka, Ruben Loftus-Cheek could've done better with a free header from a corner and Antonio Rudiger skied a volley.
However, the visitors may have also won it but Fred failed to execute a chip from the edge of the box as both sides shared the spoils in a match that saw Cristiano Ronaldo on the bench to begin with.
The drama started before the match with caretaker boss Carrick opting to bench Ronaldo to begin with and it was looking to have backfired with Man United making a slow start.
They needed David de Gea to bail them out early on as he kept out Hudson-Odoi's early effort.
Premier League leaders Chelsea were then restricted to more long-range efforts but still came close as Rudiger hit the bar from distance while Reece James' bending free-kick threatened to bounce into the top corner before De Gea clawed it away.
And Man United took the lead against the run of play on 50 minutes when Jorginho was dispossessed by Sancho on the halfway line after trying to control a looping ball - the England star then calmly bore down on goal and slid the ball past Edouard Mendy.
Carrick then hooked Sancho off on 63 minutes as Ronaldo entered the fray, but five minutes later the scores were level.
Jorginho stepped up and slotted into the corner of the net after Wan-Bissaka booted Silva's ankle in his attempts to clear the ball.
The home side then had the lion's share of the chances with Werner, Loftus-Cheek and Rudiger all having their moments but neither side was able to find the winner.