Eden Hazard headed in a first-half goal for Chelsea at Upton Park before the leaders rode their luck to stay on course for a second trophy this season to go alongside the League Cup they captured on Sunday.
"My team were brothers on the pitch and that is important if you are to win the most difficult league in the world," Chelsea manager Jose Mourinho said.
Second-place Manchester City stayed in touch with Chelsea by beating Leicester 2-0, although goals by David Silva and James Milner masked an unimpressive display by the champions, who dropped captain Vincent Kompany. Chelsea has a game in hand.
Behind the top two, the race for Champions League qualification remains tight following victories for Arsenal, Manchester United and Liverpool that kept the teams separated by three points.
Seventh-place Tottenham also won, beating Swansea 3-2 in a match that started in alarming circumstances when Swansea striker Bafetimbi Gomis collapsed in the centre circle in the seventh minute.
White Hart Lane fell silent as Gomis received treatment by medical staff, before being carried off and taken to hospital as a precaution. The France striker, who has a history of fainting during games, said hours later that he was "feeling well" and that he was stressed and suffering from fatigue because of his father's health.
Gomis fell to the ground in a similar area of the field to where Fabrice Muamba suffered a cardiac arrest playing for Bolton against Tottenham in an FA Cup match in 2012.
Man United left it late against Newcastle as Ashley Young capitalized on goalkeeper Tim Krul's error to score an 89th-minute goal in a 1-0 win. The game was marred by an angry exchange between Newcastle's Papiss Cisse and United's Jonny Evans, during which the players appeared to spit at each other.
United stayed a point behind third-place Arsenal, which beat Queens Park Rangers 2-1 through goals by Olivier Giroud and Alexis Sanchez. Liverpool comfortably beat Burnley 2-0 at Anfield thanks to goals by Jordan Henderson and Daniel Sturridge to stay unbeaten since December — a run of 12 games — and within two points of United ahead of their meeting on March 22.
Tottenham is six points off the top four.
Elsewhere, Everton's woes continued with a 2-0 loss at Stoke, which climbed to eighth after a third straight win. Everton is winless in five matches and six points above the relegation zone.
On paper, the trip to Arsenal on April 26 looks to be the only difficult away fixture left for Chelsea. With its home form imperious under Mourinho, Chelsea is closing in on the title and a trophy double in the Portuguese coach's second season in his second spell in charge.
Hazard has been one of the team's best players this season and he was the difference against West Ham, meeting a cross by Ramires with a header from what looked to be from an offside position.
Chelsea relied on some great saves from Thibaut Courtois to preserve the lead.
"It was not the best game to play after the final," Mourinho said. "The final is more than a game, because of tension, pressure and emotions. Some periods (against West Ham), we had to defend with everything."
Kompany started on the bench after a number of below-par displays at centre back, but City still struggled against a team bottom of the standings. Silva pounced from close range to put City ahead after an unconvincing start at Etihad Stadium and Milner came off the bench to settle nerves in the 88th minute.
After losses to Barcelona in the Champions League and Liverpool in the league, City manager Manuel Pellegrini said: "I think always when you don't have the result, you need the next game is very difficult. That is why the most important thing was to win the three points."