Chelsea moved back to the top of the Premier League and made it nine successive league wins as Diego Costa scored the winner against a stubborn West Brom.
The Spain striker took advantage of a mistake by a hesitant Gareth McAuley in the 76th minute to rob the defender of possession and curl a brilliant left-foot shot past Ben Foster.
West Brom had looked like earning a point after restricting the Blues to just one other shot on target, a 30-yard David Luiz free-kick.
Chelsea also came close through an N’Golo Kante shot that deflected off Pedro and rolled just wide of the post.
The Baggies had early chances through a Chris Brunt shot that fizzed wide and Salomon Rondon shooting across goal.
Chelsea move three points ahead of Arsenal while West Brom stay ninth.
Costa matches 2015-16 total after 15 games
Chelsea had scored 22 in their previous eight league victories but looked likely falling victim to a defensive masterclass from Tony Pulis’ side until Costa struck.
The Blues had been frustrated by West Brom’s compact defence, which hurried and hassled them from the start and pressed high up the pitch, restricting them to speculative shots from long range until McAuley’s error.
The 37-year-old Northern Irishman, who had been booked, had plenty of time to clear a hopeful Cesc Fabregas pass down the line but delayed fatally, allowing Costa to force him off the ball and run inside.
It was the 28-year-old’s 12th league goal of the season, matching last season’s total.
Job so nearly done by West Brom
West Brom had won three of their previous four league games, drawing the other, and if they had been able to hold out for another 14 minutes another point would have lifted them into sixth position.
Craig Dawson and Jonny Evans led a superb defensive display, allowing Eden Hazard and Pedro little space in which to roam and spread the play.
The Baggies had failed to win at Stamford Bridge in the league since September 1978 but began the brighter, with Brunt heading over before his 25-yard shot.
As the game continued their ambition was largely restricted to keeping Chelsea out but they were doing that comfortably until McAuley took the wrong option when he should have belted the ball into row Z.
Dawson picked up his fifth booking of the season for pulling back Costa off the ball and will now miss Wednesday’s home game against Swansea.
Man of the match – Jonny Evans (West Brom)
What they said:
Chelsea boss Antonio Conte told Match of the Day: “For sure there was relief, it was a tough game and we prepared for this situation. West Brom is a tough team, a physical team who are difficult to break down. It was a good win and now we must continue.
“We have won nine in a row which is fantastic because this league is very tough. We are working very well.
“I think West Brom prepared well defensively and tried to close every space. This game, if you find the goal quickly, you can have an easier game. When you don’t find the goal, it becomes more difficult but we were very good to find in the right moment to do it.”
West Brom boss Tony Pulis told Match of the Day: “I was happy all the way through the game. They play a different system to most teams and we’d worked on a structure to beat them.
“It’s disappointing because Gareth [McAuley] has got to deal with it. He’s made a mistake and we move on. We don’t really want to criticise anyone. Our structure and organisation was very good.
“One mistake, one chance and the fella puts it away – that’s the difference in quality that separates the teams at the top.”
Chelsea go to bottom side Sunderland on Wednesday (19:45 GMT) before a London derby at Crystal Palace on Saturday at 12:30.
West Brom host Swansea on Wednesday (20:00) and then have another home game against Manchester United on Saturday at 17:30.