Peter Crouch had sent the visitors ahead in the 79th minute of the contest, but West Ham snatched a point at the death courtesy of a left-footed strike from Carroll in the final minute of normal time.
The result has seen West Ham move seven points clear of the relegation zone, while Stoke remain 19th in the Premier League table - five points off 17th-placed Swansea City with four matches to play.
West Ham boss David Moyes named an unchanged team from the one that started the 1-1 draw at Chelsea last time out, but Carroll and Manuel Lanzini were back on the bench for the Hammers following injury.
It was West Ham that had the game's first shot on target in the third minute, and Arthur Masuaku's low effort was well saved by Potters goalkeeper Jack Butland, before Joe Hart kept out an attempt from Ramadan Sobhi down the other end.
Butland was again called into action in the seventh minute to keep out a deflected effort from Marko Arnautovic as half-chances continued to arrive in the capital.
Indeed, Mortiz Bauer also registered a shot on target for the visitors in the 12th minute as the wing-back brought a decent save from Hart, before Aaron Cresswell's long-range free kick was beaten away by Butland five minutes later.
Arnautovic was next to come close for West Ham just past the 30-minute mark when the Austrian missed the far post following good work from Joao Mario in the final third.
Mame Biram Diouf then tested Hart with a powerful strike down the other end of the field, before Butland made a brilliant save to keep out a close-range Arnautovic attempt 10 minutes before the break.
The final piece of first-half action saw Mark Noble test Butland from distance as the two teams headed down the tunnel at 0-0.
West Ham had the ball in the back of the Stoke net in the 55th minute when Arnautovic headed past Butland from close range, but the offside flag saw the home side's celebrations cut short.
Stoke had a huge chance to take the lead moments later when Bauer drove down the right before delivering a fine cross into Diouf, but the striker fired over the crossbar from close range.
The Hammers again had the ball in the back of the Stoke net in the 66th minute courtesy of Edimilson Fernandes, but once again it was disallowed as Arnautovic was adjudged to have been interfering with play.
Butland then kept out a curling Cresswell free kick as the pressure from the home side continued.
It was Stoke that took the lead in the 79th minute, however, when Crouch fired home from close range after Hart was unable to gather a strike from Shaqiri.
The response from West Ham was strong, and Mario fired over the crossbar in the 84th minute as the hosts, who brought Carroll, Javier Hernandez and Lanzini off the bench, threw everything at their opponents.
Carroll ultimately levelled the scores with a brilliant left-footed finish in the 90th minute, and the home side thought that they had won it when Hernandez struck past Butland moments later, but the Mexican's effort was chalked off for a Carroll handball as the points were shared at the London Stadium.
WEST HAM (3-4-3): Hart; Rice, Ogbonna, Cresswell; Zabaleta, Kouyate, Noble, Masuaku (Lanzini 81'); Fernandes (Hernandez 76'), Arnautovic, Mario (Carroll 86')
STOKE (4-2-3-1): Butland; Zouma, Shawcross, Martins Indi, Pieters; Allen, Badou; Bauer (Crouch 70'), Shaqiri, Ramadan (Cameron 62'); Diouf (Ireland 87')