Branislav Ivanovic opened the scoring at The Hawthorns, but the Blues were unable to build on that advantage and saw Victor Anichebe step off the bench to restore parity.
The Baggies, having slipped into the bottom three over the weekend, set out to contain and frustrate their high-flying opponents, and they executed their game plan perfectly until switching off seconds before the interval.
Willian swung over a corner from the right, David Luiz touched the ball on at the near post and Ivanovic was able to escape his marker and turn home from close range.
West Brom offered much more of an attacking threat after the restart and, having been knocking on the door for some time, saw Anichebe haul them level three minutes from time as he glanced a Saido Berahino cross in off the post.
It has been the desire of new head coach Pepe Mel - who remains without a win as Baggies boss - to see his players give the opposition not a minute's respite, and Chelsea were rarely allowed any time on the ball at any stage.
That was underlined by the minimal number of chances that came their way during the opening half prior to Ivanovic's injury-time effort.
The key ones fell Willian's way as he first saw a fierce 27th-minute drive flash just over the angle of bar and post.
Three minutes from the break he picked up a loose ball on the edge of the area before chesting it down and sending a half-volley dipping over the goal.
Then came Ivanovic's goal - a blow for Albion, although they had conjured just one chance of note in the first period.
From Willian's corner into the near post, centre-back David Luiz was left unmarked to flick the ball on with his right foot to the far post where Ivanovic slotted home from three yards.
The first half was most notable for the boos that rang in the ears of Ramires - playing in place of Frank Lampard in the only change to the Chelsea team that beat Newcastle.
Ramires was the player who contentiously earned Chelsea a penalty in the 2-2 draw at Stamford Bridge in October, when Albion were seconds away from a shock victory.
The Albion fans certainly had not forgotten that moment as Ramires' every touch was greeted with jeers and catcalls.
After the break Willian came the closest to extending Chelsea's lead, but the Brazilian found Ben Foster in fine form.
As the half wore on the home side finally found some impetus up front and began to create opportunities, with James Morrison firing wide, Thievy flashing a shot through the six-yard box and Chris Brunt hammering a half-volley past the post.
Anichebe was introduced with 17 minutes remaining in an effort to provide greater cutting thrust, and he delivered in dramatic fashion after getting in front of David Luiz to turn in a pinpoint cross from Berahino.