It looked as though Jose Mourinho was set to suffer his first home Premier League defeat in charge of Chelsea before referee Andre Marriner pointed to the spot deep into stoppage-time after Ramires went down easily in the area under a challenge from Steven Reid.
West Brom had come from behind to take the lead after Samuel Eto'o had seized on a moment of hesitation from Liam Ridgewell to open the scoring on the stroke of half-time.
Shane Long equalised with a header on the hour mark and Stephane Sessegnon then made it 2-1 when Petr Cech was at fault in failing to keep out his low shot.
Mourinho, who had not lost any of his previous 65 Premier League home games in two spells as Blues manager, winning 51, recalled Hazard to the side after leaving the Belgian midfielder out against Schalke when a lost passport saw him return late for training.
The visitors, with manager Steve Clarke taking on his old club, broke on eight minutes but Morgan Amalfitano dragged his shot wide.
Chelsea were awarded a free-kick on 14 minutes after Oscar was upended by Claudio Yacob. Frank Lampard smacked the ball straight into Youssouf Mulumbu, with Long racing away on to the rebound down the left flank before he was tripped by Lampard, which resulted in a yellow card for the Chelsea midfielder.
Oscar took a free-kick from 25 yards after a foul by Yacob on Hazard and curled the ball up over the wall, but Baggies keeper Boaz Myhill was alert to tip it over the crossbar.
Chelsea continued to press, with Oscar smashing the ball high into the Shed End from 18 yards after a quick break.
The hosts took the lead on the stroke of half-time. Hazard cut in from the left and drilled in a low shot, which Myhill did well to push away at full strength.
However, Ridgewell dithered instead of hacking the loose ball away and Eto'o snuck in on the blind side again to slot past the keeper into the far corner.
Eto'o, who scored a similar opportunist goal against Schalke off the goalkeeper's error in midweek, wheeled away in celebration and was booked for his troubles.
Chelsea opened up West Brom at the start of the second half with a wonderful sweeping 30-yard pass from Oscar which floated over to Hazard, charging into the area down the left.
However, the Belgian's first touch was heavy, which pushed the ball on through to a grateful Myhill.
West Brom were almost level on 56 minutes when Amalfitano's deep cross from the right was headed against the outside of the far post by Long.
The visitors did equalise on the hour, though. A corner from the right was met with a power header from Gareth McAuley, which Cech did well to beat away at point-blank range.
As the ball looped up in the six-yard box, with the Chelsea keeper on the floor in the goal, Long climbed highest through the bodies to nod in his first of the season.
Mourinho reacted by changing Lampard for striker Demba Ba. However, it was the visitors who went ahead on 68 minutes.
The Baggies broke quickly down the left, with Ridgewell in support of the counter-attack and he fed Sessegnon at the edge of the penalty area.
The Benin forward sidestepped his marker and sent a low shot goalwards, which squirmed through Cech's grasp and into the net.
Mourinho made his final throw of the dice when Cesar Azpilicueta was replaced by John Obi Mikel and Juan Mata came on for Oscar.
Myhill denied Branislav Ivanovic with a smart save down to his right as Chelsea pressed for an equaliser before Willian headed over.
However, West Brom were left crestfallen in the fourth minute of stoppage-time when Reid was adjudged to have pushed over Ramires, and Hazard slotted past Myhill to snatch Chelsea a draw.