In a thrilling match, West Brom looked to be heading for their first win back in the Premier League after racing into a commanding lead inside the opening 30 minutes at The Hawthorns.
A mistake by Marcos Alonso led to the hosts’ first, Matheus Pereira feeding Callum Robinson to produce a classy finish past Willy Caballero, who was starting in place of dropped £71m keeper Kepa Arrizabalaga.
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.
Remarkably, it was quickly 3-0 as Kyle Bartley was left unmarked to tap home inside the six-yard box after the visitors failed to deal with a corner.
But Frank Lampard’s side rallied after the break and Mason Mount reduced the deficit 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.
Although West Brom boss Slaven Bilic was unhappy the goal stood because of a Havertz handball in the build-up.
He said: “It’s not maybe handball – it is handball. It’s so obvious I don’t even want to talk about it.”