However, Eden Hazard stepped up in stoppage time to convert a controversial penalty.
Below, Sports Mole has looked back over the contest to determine if the result was a fair one.
On target 7
On target 3
Was the result fair?
West Brom will feel hard done by and they have every right to do so. It appeared that they were heading for all three points, only for a poor stoppage-time decision made by the referee saw the match drawn. Without that, Chelsea would have been defeated. For all their hard work and endeavour, West Brom did enough to take all three points.
Manager Jose Mourinho will know that his side got lucky today, regardless of what he tells the media. They had plenty of possession, but playing at Stamford Bridge one wouldn't expect anything less. What they did with the ball was very disappointing, though. There was a lack of tempo about the Blues, especially in the final third and the last pass was often a poor one.
West Brom's performance
The controversy aside, Steve Clarke has every reason to be proud of his players. He sent them out with a plan to frustrate the hosts and it appeared that it was going to work. They defended extremely well and particularly during the second half they broke with purpose, which resulted in two goals. What's more, they showed that the display that they produced at Old Trafford a few weeks ago was not a one off - they are capable of mixing it with the division's biggest teams.
Sports Mole's man of the match
Gareth McAuley: This could have quite easily been given to McAuley's fellow West Brom centre-back Jonas Olsson because both of them were fantastic throughout the 90 minutes. They blocked virtually every shot and headed clear the majority of crosses in the box. McAuley gets the nod, though, because it was his header that resulted in West Brom's first goal.
Liam Ridgewell looked an odds-on certainty to get this award, but he has been let off the hook by Petr Cech. The Chelsea goalkeeper is regarded by many to be one of the best in the world in his position, but he won't want to see Sessegnon's goal again. It was a scuffed effort from the West Brom playmaker, but it was allowed to squirm into the net as Cech failed to get a firm hand behind the ball.
With 90 minutes played, Andre Marriner could have been pleased with his performance. However, he ruined all of that in stoppage time by awarding Chelsea a penalty that seemed clear to everybody wasn't even a foul, let alone a spot kick! That error had the biggest impact on the whole game. Perhaps he was swayed by the crowd, but it was a major mistake from someone who is supposed to be one of England's better officials.
Chelsea: After the international break, the Blues make the trip across London to take on rivals West Ham United.
West Brom: There is also a derby match for West Brom, who will play host to Aston Villa on Monday, November 25.