Referee Andre Marriner awarded the controversial spot-kick in the fourth minute of stoppage time for a challenge by Steven Reid on Ramires. Hazard converted for his fourth goal of the season on his return to the side after he was dropped for the midweek UEFA 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.
Sessegnon's strike followed Shane Long's leveller 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.
Samuel Eto'o opened the scoring for Chelsea on the stroke of half-time as he robbed Liam Ridgewell at the back post. Long hauled the sides level just after the hour 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, but the striker was unable to convert any of the 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.
In the last minute of the first half, Eto'o finally found the net.
Hazard saw a low shot parried by Myhill, 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 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 saw his bullet header saved by Petr Cech, but Long rose highest at the back post to head home.
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.
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