The Blues overcame a stern test of their title credentials thanks to Eden Hazard’s first-half header and a string of fine saves from goalkeeper Thibaut Courtois.
West Ham pressed forward all night but could not find the breakthrough as Jose Mourinho’s men defended resolutely, needing crucial interventions from the imperious Courtois and then Gary Cahill to take all three points back across London.
Mourinho, who has never tasted defeat at West Ham, made just two changes to his Capital One Cup-winning side for the trip to Upton Park with Courtois and Oscar restored to the starting line-up but it was West Ham, who lost Winston Reid to injury in the eighth minute, who looked the more likely to break the deadlock in the opening stages.
Kevin Nolan was brought in to replace Alex Song for the hosts and he was instrumental in creating West Ham’s first chance in the 18th minute, but Cheikhou Kouyate’s shot was smartly saved by the onrushing Courtois.
West Ham were causing John Terry – booked for pulling back Enner Valencia – and Cahill plenty of problems but could not take advantage as Diafra Sakho miskicked Kouyate’s pass when shooting from inside the penalty area.
For all their good work, a West Ham lapse in concentration was punished as Hazard ghosted in unmarked behind the Hammers defence to head Ramires’ cross past Adrian from five yards out in the 22nd minute.
The goal drew the sting out of the home side and they were caught out again as Hazard released Diego Costa on goal, only for Carl Jenkinson to make an excellent last-gasp tackle.
Minutes later, Jenkinson was in the thick of the action again but this time at the other end. The on-loan full-back whipped in an excellent cross from the right to find Sakho, but the striker headed the ball straight at a thankful Courtois.
West Ham continued to test the Chelsea back four after the break but when they managed to beat Terry and his troops, they could not get past Courtois, who got his fingertips to Sakho’s close range shot.
The visitors thought they had wrapped up all three points as Ramires cut back on his left foot in the penalty area, but his shot rebounded off the post and into the grateful arms of Adrian.
The Brazilian had another chance to extend the Blues’ advantage minutes later but this time it was Adrian with the heroics as he saved the header with his legs.
However, in a pulsating game in east London, it was West Ham who were piling on the pressure late on as Downing breezed past Branislav Ivanovic to pick out Sakho, who failed to direct his free header on target.
Chelsea were dropping deep in attempt to soak up the pressure but it nearly back-fired when Courtois made his only error of night, spilling the ball to Sakho, before Cahill intervened.
Substitute Willian had one final chance to wrap things up for the league leaders in the dying stages but Aaron Cresswell managed to clear off the line, while at the other end Nene’s shot was well blocked by Terry to typify Chelsea’s defending on the night.
The Hammers now have one win in 11 league games and have slipped to 10th in the standings but for Chelsea, it is a crucial win to stay five points clear of Manchester City with a game in hand.
Mourinho can now focus on next week’s Champions League last-16 second leg with Paris St Germain safe in the knowledge his side are in an excellent position to add a first league title in five years to Sunday’s Capital One Cup success.
West Ham: Adrian (7), Jenkinson (7), Tomkins (7), Reid (5), Cresswell (7), Noble (6), Kouyate (8), Nolan (6), Downing (6), Valencia (6), Sakho (5).
Subs used: Collins (6), Nene (5).
Chelsea: Courtois (9), Ivanovic (7), Cahill (7), Terry (8), Azpilicueta (7), Ramires (7), Zouma (7), Fabregas (6), Oscar (5), Hazard (8), Costa (7).
Chelsea subs: Willian (6), Drogba (5), Remy (5).
Man of the Match: Thibaut Courtois
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