The Belgian struck from the spot late on to prevent a first Premier League defeat for Jose Mourinho, with Shane Long and Stephane Sessegnon having put the Baggies ahead.
Stephane Sessegnon thought he had won the game for the visitors with his 68th-minute strike, but the three points were snatched away from them by the late equalizer.
Sessegnon's strike followed Shane Long's leveller from a Samuel Eto'o opener, as former Chelsea player and assistant manager Steve Clarke looked set to end Mourinho's unbeaten run at home in the Premier League, which has now been extended to 66 games.
Mourinho – taking charge of his 100th home game in all competitions as Chelsea manager - recalled Hazard after he was dropped from the midweek Champions League win over Schalke. Frank Lampard was the only other change from Wednesday's victory, the England international replacing John Obi Mikel.
The visitors welcomed Reid back for the injured Billy Jones and Claudio Yacob for James Morrison but there was no starting spot for Saido Berahino, despite his goal in the 2-0 win over Crystal Palace last weekend.
Chelsea began the stronger of the two sides and created good openings for Eto'o, though the striker was unable to convert any of the opening four chances he had.
Oscar went closest to breaking the deadlock after half an hour from a long-range free-kick but Boaz Myhill reached up to his left to tip the ball over the crossbar.
Yet, in the last minute of the first half, Eto'o finally found the net. Hazard saw a low shot parried by Myhill and the loose ball fell to Ridgewell - but he dallied in possession and the striker wrapped his leg around the defender to fire into an empty net.
West Brom, however, came out for the second half with renewed vigor and leveled just after the hour. Long grabbed the equalizer from close range minutes after both he and Jonas Olsson had missed chances.
The Republic of Ireland international made no mistake with his second opportunity in as many minutes as he reacted quickest to a Cech save off a corner kick, rising up and heading home from three yards.
And Sessegnon put the visitors ahead seven minutes later after receiving a pass from Ridgewell as he side-stepped the challenge of John Terry and slotted the ball under Cech.
There was late drama, however, as Reid was adjudged to have bundled Ramires to the floor, with Hazard making no mistake from 12 yards. Not for the first time, Mourinho's blushes were saved.