United went into the game having won just two of their last 16 meetings with Chelsea and that run looked set to continue as the home side dominated the ball early on in the capital.
Maurizio Sarri's side controlled possession, but United were doing a good job of denying them in open play, before they shot themselves in the foot with a moment of madness from a set-piece.
Paul Pogba completely switched off as Willian swung in a corner from the right, allowing Antonio Rudiger to breeze past him and into space to plant a free header beyond David de Gea and into the far corner to open the scoring.
There were few other efforts on goal in what was a first half for the purists, whilst the start of the second period looked to be more of the same.
The 'Blues' continued to control the ball and have the better of the game and went close when Jorgino and Alvaro Morata, preferred up front to Olivier Giroud, combined, but the Spaniard could only fire into the arms of de Gea after expertly spinning his man on the edge of the box.
They were made to regret that miss with the second half just ten minutes old as United leveled against the run of play.
Juan Mata was denied by a fine save from Kepa Arrizabalaga, but there was nothing the Basque could do just seconds later as the ball bobbled into the path of Anthony Martial to drill home from close range.
That goal boosted the visitors, who came out of their shell in the 10 minutes that followed.
David Luiz wasted a glorious chance to restore the lead when he ghosted in to meet Willian's free-kick from the right, only to flick his header wide of the far post having been afforded the freedom of the Stamford Bridge penalty box.
Chelsea has just about wrestled back control of the game at this point, with N'Golo Kante going close to a goal on his 100th appearance for the club, only for de Gea to produce a strong right-handed stop to deny him a landmark goal.
With the goal poised on a knife-edge, there was always the risk that United could unpick the hosts on the counter and so it proved as United took the lead with just 17 minutes to go.
Mata nicked the ball away from Luis down the right and fed Marcus Rashford. He picked out Martial and whilst his touch appeared to have let him down but he was able to recover to curl low into the far corner from just inside the box to give United the lead.
Chelsea pressed hard in the time remaining to find a winner, but were still trailing when the fourth official indicated that there would be six minutes of added-on time.
That proved to be the perfect amount for Chelsea, who leveled deep into stoppage time through Ross Barkley. Luiz saw another header crash back off the post and whilst de Gea did well to deny Rudiger's follow-up, there was nothing he could do to prevent Barkley from stroking home the loose ball.
The strike sparked ugly scenes on the two benches as Jose Mourinho reacted angrily to being goaded by the Chelsea coaching staff, the Portuguese having to be restrained by stewards.
Mike Dean eventually called time on the game as it ticked into its 100th minute, with Chelsea doing just enough to maintain their unbeaten record this season.
For United, it was a case of what might have been as their long run without a win at Stamford Bridge continues.
October 20, 2018