First-half goals by Shinji Okazaki and Riyad Mahrez put them in command at Upton Park and although Dimitri Payet halved the deficit Leicester deservedly made it two wins from two to edge ahead of Manchester United on goal difference.
Romelu Lukaku's double and a gem from Ross Barkley helped Everton to a 3-0 win at Southampton as they joined Swansea City on four points from two games.
Swansea's new signing Andre Ayew scored for the second week running as they cruised to a 2-0 home win against Newcastle United and he will be eyeing more chances next week when the Welsh club travel to Sunderland.
Dick Advocaat's Sunderland are already firmly established as relegation favourites after they followed up an opening day horror show at Leicester with a 3-1 home loss to promoted Norwich City on Saturday to stay rock bottom.
"Together we have to find out if we can find the solution," Dutchman Advocaat told the BBC. "Expectations were high, we have to find the reason otherwise we have no chance."
With the new season still shaping up, some of the players making up the supporting cast to the so-called superstars are making an early impression.
None more so than Leicester's Mahrez.
The 24-year-old Algerian's powerful finish doubled Leicester's lead in the 36th minute to take his tally in two matches to three. Okazaki had nodded Leicester ahead 10 minutes earlier after keeper Adrian, sent off late on, had blocked his initial effort.
Leicester survived West Ham's fightback to continue Claudio Ranieri's perfect start since taking over from Nigel Pearson under who's command Leicester won seven of their last nine games last season to complete a great escape.
"All the match was good for us. We are playing well. All the players are playing like a team, they play with the ball on the ground and it is important to increase our stamina and fitness, and also our mentality," Ranieri told the BBC.
Another player catching the eye is Swansea's Ayew.
After his goal against champions Chelsea last weekend the Ghanian striker, signed on a free transfer, netted a 52nd minute header to seal the points after Bafetimbi Gomis, also a scorer against Chelsea, scored a clever opener. Newcastle were not helped by a red card for Daryl Janmaat after 41 minutes.
"We dominated the whole game from start to finish," Swansea's young manager Garry Monk said.
"When the red card does come it impacts on the dynamic of the other team more and they sat back after that."
Lukaku has already established himself as a top flight marksman and the Belgian was at his powerful best as Everton cruised past listless Southampton.
The former Chelsea player headed in Arouna Kone's cross after a dazzling counter-attack in the 21st minute and his raw power unhinged Southampton's defence when he exchanged passes with Barkley before firing his second just before halftime.
Barkley's curler completed victory late on with manager Roberto Martinez describing the duo as "unplayable".
Goals from Eric Dier and Nacer Chadli put Tottenham Hotspur 2-0 up against Stoke City at White Hart Lane but they still await their first win of the season after Marko Arnautovic's penalty and Mame Biram Diouf struck late on for the visitors.
Watford drew 0-0 at home with West Bromwich Albion.
Manchester City host Chelsea at the Etihad on Sunday while Crystal Palace entertain Arsenal in a lunchtime kickoff.
(Editing by Ed Osmond and Justin Palmer)
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