Andy Carroll rescued a point for West Ham and denied Stoke a vital victory with a last-minute equaliser in a 1-1 draw at the London Stadium on Monday night.
Stoke had to wait until the 79th minute to make the breakthrough as Peter Crouch took advantage of a mistake from West Ham goalkeeper Joe Hart to turn home from close-range.
However, fellow substitute Carroll came off the Hammers bench to volley home Aaron Cresswell's inch-perfect cross to keep David Moyes' side seven points above 19th-placed Stoke in the race to avoid the drop.
It could have been worse for Stoke but Javier Hernandez had an even later goal disallowed for a foul by Carroll.
Sky Bet now make Stoke as short as 1/12 (from 1/9 before kick-off) to go down.
West Ham have been pushed out from 14/1 to 18/1 in the online bookmaker's relegation odds.
Post-match reaction
Peter Crouch bemoaned the loss of two vital points as Stoke missed a chance to close to within three of 17th-placed Swansea.
He told Sky Sports Main Event: "We had five minutes left (when Carroll scored) and it would have been a vital win for us, but coming here and getting the draw is still a good result.
"It would have done us the world of good to get the three points but it was a great finish by Andy.
"Since this manager's come in we've shown a lot of character and have stopped shipping goals.
"There's winnable games left and if we win three of them then who knows what will happen?"
Paul Lambert is desperate for Stoke's fortunes to turn.
Lambert admits Stoke's next match, at home to Burnley, is now a must-win game that will "put the cat among the pigeons" at the bottom of the table should they triumph.
He added: "I thought we deserved something from the game, we played a really good game and if we keep playing like that we will win games.
"If there is a little bit of Lady Luck it hasn't come our way but the performances have been very good. If they had played like that since August I wouldn't be here and we wouldn't be in this position."
West Ham boss David Moyes said: "He (Joe Hart) had two similar shots in the first half and took them comfortably, so it was a surprise that it spilled out.
"If you are a goalkeeper it's going to happen. It meant we had to change things after we had been dominating the game.
"Our subs all played well. I don't know if we will get Andy fit enough for 90 minutes, but if he can get 20 or 30 minutes that would be handy."
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