Manager Brendan Rodgers made nine changes from the side that lost 4-0 at home to Liverpool less than 48 hours earlier, but still had too much for a fragile West Ham side.
Leicester City shook off chastening back-to-back defeats with a 2-1 victory at West Ham United to renew their distant chase of Premier League leaders Liverpool on Saturday.
Manager Brendan Rodgers made nine changes from the side that lost 4-0 at home to Liverpool less than 48 hours earlier, but still had too much for a fragile West Ham side with goals by Kelechi Iheanacho and Demarai Gray closing the gap to 10 points.
Gray had an early penalty saved by West Ham's returning keeper Lukasz Fabianski but Iheanacho headed Leicester into a deserved lead in the 40th minute.
West Ham's one flowing move of the first half saw them level with Pablo Fornals slotting home.
But there was a lack of belief from a West Ham side without a home win since September and Leicester regained the lead in the 56th minute when Gray finished off a superb counter-attack.
Second-placed Leicester, without the Premier League's top striker Jamie Vardy who was excused duty after becoming a father for the third time, could have won by a bigger margin as they moved four points clear of Manchester City.
After shipping seven goals in defeats by City and Liverpool, Leicester look back on track, despite having played two more games than the European champions.
A second successive Christmas defeat for West Ham leaves them one point and one place above the relegation zone with manager Manuel Pellegrini now under even more pressure ahead of a crucial New Year's clash with Bournemouth.
Rodgers' decision to rotate his squad looked to be a gamble but, instead, it showed the depth of his squad with Gray one of the players to shine, having been given a rare starting slot.
"We controlled the game, put out a fresh team but it paid off," Gray, whose penalty was saved by Fabianski, said.
"If you're not playing so much you have to try and stamp your mark and get yourself in the team. It just shows the quality and depth we've got in the team."
West Ham made seven changes from the side that lost at Crystal Palace on Boxing Day, but unlike Leicester's stand-ins, they produced a meek performance in front of an apathetic crowd.
The return of Fabianski after missing 11 league games with injury was a boost for the hosts but he had a mixed start.
First, he clattered into Iheanacho to concede a penalty but redeemed himself by saving Gray's spot kick.
The let-off did not ignite the home side and they fell behind when James Justin's deep cross was kept in play by Ayoze Perez and Iheanacho nodded in from close range.
Hundreds of West Ham fans went for an early halftime soother and missed the sweeping move that ended with Felipe Anderson squaring for Fornals to slot home.
That was as good as it got for the hosts. In the 56th minute, Leicester sprung out of defence, Perez sliced through West Ham's midfield and played the perfect pass for Gray to guide his shot past Fabianski.
An air of resignation then swept the London Stadium and, despite the home fans' unflagging support, their gloom at the final whistle was in stark contrast to the Leicester fans' joy.