Reid would not only be the latest Hammer to suffer another injury this season, as solid holding midfielder Pedro Obiang had to be stretched off in the 67th minute with a possible groin injury. Hope was first restored by a skilful Manuel Lanzini free kick, then deflated by Jamie Vardy's goal.
Andy Carroll headed the set-piece back to Ayew, whose header had enough power to go through Schmeichel.
However, Kasper Schmeichel made two tremendous saves to deny Carroll from close range late on and ensure a fourth straight victory for the Foxes under new manager Craig Shakespeare.
"We want to move away from the relegation zone because it is tight down there but we can't look too far ahead".
Leicester opened the scoring in unorthodox fashion as Riyad Mahrez whipped a low cross into the area from the right flank, but the ball missed everyone in the box and settled nicely into the side netting past West Ham goalkeeper Darren Randolph to give the visitors the lead. In the last five matches of West Ham United, the team lost their two matches, two drawn and a win to Southampton.
Leicester are unbeaten in five matches in all competitions against West Ham, winning four and drawing one.
And it nearly brought about a fourth goal just before the hour - Shinji Okazaki pouncing on a loose ball before feeding Vardy through on goal, only for the England striker to slice wide under pressure from Darren Randolph.
However, the second half was more reminiscent of Leicester's problems at the start of this year.
They doubled it just two minutes later, as this time Robert Huth found himself on the end of an exceptional outside-of-the-boot flick from Mark Albrighton for an easy finish, stunning the West Ham faithful.
West Ham are 11th in the Premier League table at the moment with 33 points from 28 matches.
The England striker goes into today's game at the London Stadium with three goals from his last four games - a marked contrast to just four in 29 under Ranieri. Permission to use quotations from this article is granted subject to appropriate credit being given to www.theeagleonline.com.ng as the source.
On Sunday, Middlesbrough will host Manchester United; Tottenham Hotspur will also host Southampton, while Liverpool is guests of Manchester City.