Kasey Palmer handed the visitors the lead against the run of play on 17 minutes, and Ola Aina almost doubled the lead before the break when he struck the top of the bar.
United struck back just after the hour mark when skipper James Weir’s shot deflected into the net, but the Red Devils had to settle for a draw in the end, which leaves them three points behind leaders Sunderland.
United start strong, but Chelsea strike first
Phil Jones and Ashley Young, who were making their returns following injuries, started the game and it was the hosts who started the brighter.
Young looked like a man on a mission and looked lively up front on his own, after having a cross deflected out for a corner, he drilled one into the side-netting.
However, against the run of play they found themselves behind in the game after Palmer’s free-kick, which seemed to be harshly awarded, sailed past Sam Johnstone in the United net.
Visitors almost double their lead
The hosts came close to getting an equaliser straight away after Guillermo Varela broke into the penalty area, but he fired straight at the 'keeper, before Aina struck the top of the United crossbar.
Palmer was denied a run at goal by Ro-Shaun Williams after the break, which, more than likely, would have ended with a clear shot on target, and quite possibly a certain goal.
United manage to find an equaliser
The hosts were beginning to get on top of their opponents, and after Donald Love came close, firing onto the roof of the net, Weir found the, well-deserved, equaliser.
Varela got forward and played the ball into the skipper, whose shot deflected off a Chelsea player and bobbled away into the back of the net.
There really was only one side in it following that goal, as the Reds hunted for a winner which would see them close the gap between themselves and the top-of-the-table.
Late chances squandered
Young drove forward and drilled a low cross into the path of Weir, but it was just out of the reach of the skipper, and the ball was cleared away from the danger area.
There was time for one more chance just inside of injury time, but Young couldn’t make the most of it, heading Joe Riley’s cross straight at the keeper.
Although the result leaves United in second place, they still have three games in hand over the Black Cats, and with three points separating the two sides, they look in contention to go on and retain their title.
Warren Joyce’s side host Middlesbrough in their next game on Monday 11 April at Old Trafford, while Chelsea travel to Manchester City on Thursday 7 April.