Tom Lawrence put the holders in front with a well-worked strike but Charly Musonda equalised and Lewis Baker hit the winner in the closing stages.
The visitors, who topped the league, began brightly with Baker's raking drive bringing a flying save out of Ben Amos within five minutes. The highly-rated midfielder then produced another effort but, again, Amos was equal to the task.
James Wilson had United's first attempt, only for it to strike Lawrence, but the two combined to great effect soon afterwards. Saidy Janko sprinted down the right to supply a precise centre that was touched off instantly by Wilson for his fellow first-team debutant against Hull City, Lawrence, who showed superb skill to set up a curling shot beyond Jamal Blackman.
The lead lasted only 10 minutes however, as Musonda cut in from the left to bury a low drive after being afforded too much space. The goalscorer provided a pass for John Swift to prod wide while the Reds' brightest moment before the interval came when Paddy McNair had a shout for a penalty following a challenge by Ola Aina.
Chelsea came out of the traps with a purpose from the restart but Amos caught a bouncing effort by Aina. Ruben Loftus-Cheek teed up Baker for a great chance, only for the no.10 to sky it high over the bar. With the chances continuing to come at Amos' end, the keeper made a fine stop with his legs to deny Loftus-Cheek after he glided through unchecked.
Wilson made way for James Weir, clearly hobbling, and the Reds struggled to test Blackman. Islam