Tammy Abraham scored a stoppage time goal to rescue a point for Chelsea who were three goals down in the first half.
West Brom looked set to grab their first Premier League victory this season as they were already ahead with three goals before the first 30 minutes of the game.
Callum Robinson produced a classy finish from Matheus Pereira’s set up in the 4th minute of the game.
Thiago Silva, who was making his Premier League debut for Chelsea, was then too casual in possession, allowing Robinson to pounce and run at goal before doubling the lead with another impressive finish.
Kyle Bartley made it 3-0 as he tapped home inside the six-yard box after the visitors failed to deal with a corner.
But in a surprising twist of events, Chelsea came back in the second half with a goal from Mason Mount from 20 yards.
Substitute Callum Hudson-Odoi set up a tense finale with a stylish finish, before Abraham, making his first top-flight start of the season, tapped home the equaliser in the 93rd minute after Mount’s shot had been saved.
West Brom now go to Southampton in the Premier League on Sunday while Chelsea are at Tottenham in the Carabao Cup fourth round on Tuesday before hosting Crystal Palace in the Premier League on Saturday.