Chelsea manager Jose Mourinho -- who picked up another trophy Sunday in the League Cup final -- had never lost to West Ham in the top flight and Belgian attacker Eden Hazard ensured three more points when he netted in the first half Wednesday at the Hammers' Upton Park.
"The game was very difficult," Hazard told Sky. "One big battle against a good team with very good players.
"It's always difficult when you don't score the second goal to kill the game. But one goal was enough. It's not always like this.
"The goalkeeper, the defense we have are very strong. It was very good."
Chelsea keeper Thibaut Courtois made a string of good saves in the second half but West Ham boss Sam Allardyce lamented his team's finishing -- plus the refereeing.
He felt Hazard's goal was offside.
"When you look back on the season and they say these things even themselves out, that's the biggest load of rubbish I've ever heard," the under pressure Allardyce told Sky.
Nigel Pearson, manager of last-place Leicester, also felt aggrieved after his team lost 2-0 to reigning league champion Manchester City.
Leicester didn't get a penalty when City striker Wilfried Bony appeared to foul Jeff Schlupp in the box in the first half or when Fernando fouled Andrej Kramaric in the second. Leicester struck the woodwork, too.
City -- reeling following back-to-back defeats to Barcelona in the Champions League and Liverpool -- only really came to life after David Silva's opener in first-half stoppage time.
Leicester's veteran keeper Mark Schwarzer thwarted City to keep it close but could do little on James Milner's 88th-minute effort.
The win was "very important because it was a very difficult week with two bad results against Liverpool and Barcelona," said City manager Manuel Pellegrini, who rested club captain Vincent Kompany.
Elsewhere, four teams vying for Champions League spots all won. Manchester United claimed all three points at Newcastle when Ashley Young took advantage of keeper Tim Krul's error in the 89th minute; Arsenal doubled third-last QPR 2-1; surging Liverpool shut out second-last Burnley 2-0; and League Cup finalist Tottenham defeated Swansea 3-2 in a game overshadowed by French striker Bafetimbi Gomis collapsing to the turf.
United defender Jonny Evans might have been fortunate to escape unpunished at St. James' Park, since he appeared to spit in striker Papiss Cisse's direction
when they clashed in the first half. Cisse then appeared to spit back at Evans.
Arsenal remained third, with United in fourth on 53 points, two better than Liverpool, four better than Southampton and six better than Spurs, who have a game in hand.
In Wednesday's other match, Stoke extended Everton's league slide by blanking the Toffees 2-0 at home.
Barcelona reaches Copa del Rey final
In Spain, meanwhile, Barcelona reached the Copa del Rey final by easing past Villarreal 6-2 on aggregate.
Holding a 3-1 lead after the first leg, Barcelona won away by the same score Wednesday, helped by Neymar's double.
Barcelona faces familiar foe Athletic Bilbao in May's finale. Bilbao advanced 3-1 on aggregate over Espanyol, prevailing in the second leg 2-0.
Barcelona topped Bilbao in the 2009 and 2011 finals.