Chelsea midfielder Jorginho calmly slotted home from the penalty spot on 85 minutes, but Casemiro arrived with a header four minutes into added time as he scored his first United goal and helped claim a share of the points at Stamford Bridge.
United were much the better side in the first half and heaped pressure on Chelsea, but they proved toothless as home goalkeeper Kepa Arrizabalaga performed well to keep the scores level. The best chances fell to Marcus Rashford and Antony, who forced Kepa into a fingertip save in the 13th minute and put a shot wide just before halftime with only the goalkeeper to beat.
"The boys gave everything but you can see that we can improve a lot in terms of our attacking play," Chelsea boss Graham Potter said.
"I thought we could have attacked a little bit better than we did. Create a few more opportunities. But it was an intense hard-fought game, two teams going at each other.
"I was really happy with the response from the team after the first half an hour. I think it's about right a point."
But United were not to be denied. Casemiro showed his quality and popped up in the box in the final moments and provided a fierce header.
The visitors were without Ronaldo, who was dropped by manager Erik ten Hag for Saturday's fixture as punishment for refusing to play as a substitute against Tottenham on Wednesday. Sources have told ESPN that Ronaldo has been available on a free transfer since the summer but they have received no interest.
The result means Chelsea and United remain in fourth and fifth, respectively, after 11 games in the Premier League.
"I would have been disappointed if we had gone without a point because we didn't deserve that. At the end of a tough week to come here, you bring the point home," Ten Hag told the BBC.
"It is difficult to say how it is now because it is so soon after the game. We have to wait 24 hours and then we will know what it is," Ten Hag said.
Information from Reuters was used in this report.