Luis Suarez's double powered Liverpool to a 4-0 victory over Fulham, and Southampton easily overcame Hull 4-1 to continue the south coast club's impressive start to the season.
Liverpool and Southampton sent Chelsea down to fourth place as the west London club was held to 2-2 at home.
Goals from Shane Long and Stephane Sessegnon put West Brom on course for a first win at Chelsea in 35 years until Steven Reid was penalized for fouling Ramires in the fourth minute of stoppage time and Eden Hazard equalized from the penalty spot.
Arsenal will finish the weekend top of the standings regardless of whether the north London club can win at Manchester United on Sunday, given its two-point lead over Liverpool.
Chelsea is four points behind the front-runners, although it could have been worse for Jose Mourinho.
The Portuguese manager's 65-game unbeaten league home record at Chelsea was looking under threat until referee Andre Marriner pointed to the spot in stoppage time.
Chelsea had gone in front through a moment of good fortune.
Hazard cut in from the left and saw his shot parried by Boaz Myhill. West Brom defender Liam Ridgewell then dithered and remained static, leaving Samuel Eto'o to score his third goal of the week.
The second half began brightly for West Brom, with Long heading against the outside of the post and then finding the target on the hour.
From Morgan Amalfitano's corner, Gareth McAuley's powerful header was pushed high into the air by Cech. As the ball came back down, Long rose to head it in.
Eight minutes later, West Brom was in front — as Ridgewell made up for the blunder that allowed Chelsea to go in front.
After breaking down the left flank, Ridgewell fed Sessegnon, whose shot easily beat Cech.
In front, but never comfortable, West Brom had to soak up sustained Chelsea pressure to protect the lead.
"Our reaction could be 'die or fight for life,'" Mourinho said. "And our team fought for life."
Fortune favoured Chelsea with the late penalty won by Ramires.
"He started going down early, he started going down before the contact," said West Brom manager Steve Clarke, Mourinho's assistant at Chelsea during his first stint in charge from 2004-07.
At Anfield, Fulham gifted Liverpool the lead when Fernando Amorebieta headed the ball inadvertently into his own goal in the 23rd minute after Steven Gerrard sent a free kick into the penalty area.
Three minutes later there was another goal, from another header — this time from a Liverpool player as defender Martin Skrtel met Gerrard's corner.
Suarez, who initially thought he diverted Amorebieta's header into the goal, then did get on the scoresheet by slotting home in the 36th.
The Uruguay striker took his tally to eight goals in six league matches since returning from a 10-game biting ban by wrapping up the win in the 54th after Gerrard turned provider again.
Southampton is just a point behind Liverpool.
Morgan Schneiderlin headed Southampton in front after 16 minutes against Hull after being set up by Adam Lallana, who then won a penalty after being brought down by goalkeeper Steve Harper.
Rickie Lambert converted from the spot on the half hour, before Lallana scored a goal of his own seven minutes later, a fine solo effort after jinking through the defence.
Yannick Sagbo pulled one back for Hull from distance early in the second half but Steven Davis completed the comfortable Southampton win in the 88th after meeting Nathaniel Clyne's cross.
At Villa Park, Aston Vila's four-game scoring drought ended when Leandro Bacuna and Libor Kozak clinched a 2-0 win over Cardiff.
There were no goals, though, at Selhurst Park as bottom-place Crystal Palace held fifth-place Everton to end a seven-match losing run. Everton goalkeeper Tim Howard started despite hitting his head before the game when he walked into the wing mirror of the team bus.
Norwich staged a second-half comeback to beat West Ham 3-1 and ease the immediate pressure on manager Chris Hughton. Norwich was booed off by its fans at halfltime at 1-0 down but was a much more cohesive unit after the break.