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.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
WEST HAM: Hart; Rice, Ogbonna, Cresswell; Zabaleta, Kouyate, Noble, Masuaku; Fernandes, Arnautovic, Mario
STOKE: Butland; Zouma, Shawcross, Martins Indi, Pieters; Allen, Badou; Bauer, Shaqiri, Ramadan; Diouf
What a free-kick this was! 🙌 pic.twitter.com/TVMsbD7vGB— West Ham United (@WestHamUtd) April 16, 2018