Coady headed home a cross from substitute Chiquinho in almost the last action of the game.
Wolves had trailed for much of the game after Chelsea's out-of-form striker Romelu Lukaku scored twice in two second-half minutes.
Lukaku, who had not scored in the league since December, claimed his first from the penalty spot in the 56th minute after a lengthy VAR check concluded he had been fouled by Romain Saiss just inside the area.
He put his second away with a fine strike from 20 metres after being put through by Christian Pulisic.
But Wolves snatched a goal back in the 79th minute through substitute Barcelona loanee Francisco Trincao and then upped the pressure, giving Chelsea, who sit third in the table and are looking to cement a Champions League spot, a nervous finish.
The Portuguese winger kept the pressure on as he had two chances to give Wolves the win after his goal.
But it was Coady who eventually scored the late equalizer for Wolves as he got on the end of a cross from Chiquinho after Trincao laid him a diagonal pass.
Chelsea remain third on the EPL standing with 67 points, fellow London team Arsenal trail behind with 63 and Tottenham at 61.
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