The Blues wasted a number of chances to make their evening more comfortable and had Thibaut Courtois to thank for making some fine savesChelsea maintained their five-point lead over Manchester City at the top of the Premier League table as they recorded a narrow win over West Ham.
Eden Hazard opened the scoring as he got on the end of Ramires' cross to head past Adrian from close range.
West Ham responded well, with Thibaut Courtois having to twice deny Diafra Sakho either side of half-time before Diego Costa hit the post for the visitors.
Sakho headed over the crossbar late on but Jose Mourinho's side held on for all three points.
The result increases the pressure on West Ham boss Sam Allardyce, who saw his side's winless run in the league stretched to six matches, leaving them 10th.
Chelsea controlled the play in the opening exchanges and Costa's close-range effort ballooned over the crossbar off his shin early on.
West Ham, who saw Winston Reid limp off in the eighth minute to be replaced by James Collins, gradually gained a foothold and Courtois - one of two changes from the League Cup final for the visitors - was quick off his line to deny Kevin Nolan after he was slipped in by Mark Noble.
But it was Mourinho's side who seized the advantage in the 22nd minute.
Hazard's pass to Cesc Fabregas was worked right to Ramires and his cross picked out the unmarked Belgium international to nod home from six yards.
Chelsea had the chance to make it 2-0 when Hazard sent Costa free in a swift breakaway, but the striker dawdled on the ball and allowed Carl Jenkinson to make a fine tackle.
Jenkinson was then involved at the other end as his pinpoint cross found Sakho in space just six yards out, but his header was too close to Courtois and an excellent chance went begging.
Shortly before the break Collins was perhaps lucky to avoid a red card for an ill-timed challenge on Kurt Zouma.
The hosts started the second half with positive intent and two dangerous Stewart Downing crosses caused confusion in Chelsea's defence.
Chelsea reasserted control from thereon and the excellent Hazard played Ramires in behind the defence, the midfielder cutting inside Collins before rolling his shot against the left-hand post.
Hazard and Ramires combined again shortly after, the latter seeing his header kept out smartly by Adrian.
At the other end Gary Cahill made an excellent challenge to deny Sahko after Courtois spilled Enner Valencia's tame effort, while Chelsea captain John Terry felt Cheikhou Kouyate should have been shown a second yellow card when the Senegal international bulldozed into him – the midfielder subsequently receiving lengthy treatment.
Both teams saw penalty shouts dismissed by referee Andre Marriner in the closing stages. First Branislav Ivanovic felt Collins had handled his shot in the area, before West Ham substitute Nene was denied a similar claim against Cahill.
It appeared as though substitute Willian would add a second for Chelsea in stoppage time, only for Aaron Cresswell to block his shot on the line - and that proved the last meaningful action as West Ham failed to score against Chelsea in the league for the fifth game running.