The Blues won out 1-0 at Stamford Bridge courtesy of Costa’s piledriver, a goal that owed everything to the Spain hitman’s hard running.
The relentless Costa robbed Gareth McAuley on the right flank before firing past a helpless Ben Foster in the Albion goal.
Chelsea can now seriously contemplate breaking their Premier League record winning streak of 11 matches, with Sunderland, Crystal Palace, Bournemouth and Stoke all still to come this month.
West Brom marked the in-form Victor Moses out of the match, boss Tony Pulis pulling a masterstroke by tasking wide man Matt Phillips with the specialist treatment.
But Costa’s 12th goal of the Premier League campaign carried Chelsea back to the top of the table, with the Blues still yet to lose in the league since their 3-0 defeat at Arsenal on September 24.
Every Tony Pulis team is built in his image, and so it proved in a rugged first half as the visitors’ stoicism rebuffed Chelsea at every turn.
Costa charged down Ben Foster’s clearance only for the goalkeeper to claim the rebound.
Hazard drove at the defence after a neat spin, pulling off a smart training-ground one-two with Costa, only to undercook the shot on goal.
Chris Brunt fired wastefully wide from 20 yards on West Brom’s first raid, and then Salomon Rondon botched a fine opening of his own creation.
The Baggies’ hitman mugged David Luiz to power into the box, opened his feet to create the space, only to drag his shot wide of the far post.
N’Golo Kante’s fluffed shot from 20 yards so nearly gifted Chelsea a goal however, as Pedro’s deflection edged just wide with Foster motionless in goal.
Costa failed to connect with Pedro’s teasing cross, before Luiz had the first effort on target with a free-kick.
West Brom held firm until the break however, with Pulis no doubt the happier of the two bosses at the interval.
Chelsea’s response to Moses being marked out of the first half was to bring Willian off the bench and into the right wing-back role. Chelsea boss Antonio Conte shifted Moses to the left of the front three, with Pedro withdrawn.
Where Pedro had consistently drifted beyond Costa to hand the hitman extra room, now Moses stuck steadfastly to the inside-left.
Even that shift for the in-form Moses proved short-lived, as he was quickly replaced by Cesc Fabregas in another roll of the tactical dice from Conte.
Chelsea continued to press, but remained unable to split West Brom’s regimented rearguard.
But just when West Brom started to hope they could hold out for the distance, up popped Costa with a classic poacher’s goal.
Costa mugged McAuley on the right flank, tore into the box and unleashed an unstoppable drive into the top-left corner.
Chelsea boss Conte insisted in midweek that Costa has started focusing purely on goals, and left the sideshow of niggling his opponents behind.
While that may not be entirely the case, the bullish forward’s goal record continues to speak for itself, cementing Chelsea’s title challenge.