The reigning champions now trail Tottenham and Liverpool by 10 points with just six games left to salvage a place in the Champions League next season.
On a weekend that saw United return to their old habits and launch a swashbuckling comeback against a crumbling City, the former United duo added to the throwback feeling by coming on and changing the game.
Three times before at Stamford Bridge Javier Hernandez had been used as a substitute and the Mexican had scored on each occasion.
The Blues had chance after chance to kill the game off, but never took them and that gave the Hammers hope.
Joe Hart was also enormous as West Ham held on for a point. The introduction of Hernandez turned a one-sided match into a thrilling end-to-end encounter, helping the visitors open up a six-point gap to 18th.
They need to hope for either Tottenham or Liverpool to make a few mistakes along the way, but I would be more anxious about Chelsea's performance.
Welbeck's victor came nine minutes from time, but there was still plenty of action to unfold at the Emirates as first Saints centre-back Jack Stephens and then Arsenal's Mohamed Elneny were sent off for separate incidents.
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I would have probably commented earlier in the season that Chelsea's last few games look like a cakewalk for the most part, but Chelsea haven't been winning the easy games.
"Chelsea were really good in the first half but we kept it to one".
"He had every reason to feel sorry for himself, to think the mountain was too big to climb, because it was the right knee, then the left knee and a year out every time". "Many games where you have a good performance, create many chances to score but you are not clinical".
Charlie Austin came off the bench to level for the Saints 17 minutes from time.
For West Ham, it was a valuable point in their fight to beat the drop, with a sizable advantage now over the bottom three.