The Belgian struck from the spot late on to prevent a first home Premier League defeat for Jose Mourinho, with Shane Long and Stephane Sessegnon having put the Baggies ahead
Referee Andre Marriner awarded the controversial spot-kick in the fourth minute of stoppage time for a challenge by Steven Reid on Ramires.
And Hazard duly converted for his fourth goal of the season on his return to the side after he was dropped for the midweek Champions League win over Schalke for missing a training session earlier in the week.
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 equaliser.
|VIEW FROM STAMFORD BRIDGE
|By Liam Twomey at Stamford Bridge
"Jose Mourinho is now unbeaten in 66 home Premier League matches - but only just. West Brom came mightily close to claiming another monumental scalp at Stamford Bridge, only for Eden Hazard's injury-time penalty to deny them and save the home side's blushes. The award looked soft and very harsh on Steven Reid, who had performed heroically - but no one of a blue persuasion will care.
"The result is nevertheless another blow to Chelsea's faltering title charge and the limp performances of senior firgures Petr Cech, John Terry and Frank Lampard will be of particular concern."
Samuel Eto'o opened the scoring for Chelsea on the stroke of half-time as he robbed Liam Ridgewell at the back post. Long then hauled the sides level just after the hour mark as the striker netted his first goal of the season from close range.
Sessegnon then put the visitors ahead with his second goal of the campaign after some sloppy defending from the hosts but Hazard rescued a point.
Mourinho – taking charge of his 100th home game in all competitions as Chelsea manager - recalled Hazard. 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 vigour and levelled just after the hour. Long grabbed the equaliser 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 head home from three yards.
Gareth McAuley then saw his bullet header saved by Petr Cech but Long rose highest at the back post to head home.
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 form 12 yards. Not for the first time, Mourinho's blushes were saved.