Dion Dublin's Leicester City debut was embroiled in controversy after he was shown a straight red card for violent conduct.
His dismissal came on 17 minutes, but West Ham failed to exploit their advantage and were themselves reduced to ten men when Rufus Brevett was show a second yellow card five minutes from the end.
City started brightly with French midfielder Lilian Nalis striking the bar from 20 yards.
But on 17 minutes Dublin was dismissed after kicking out at Brevett. The West Ham full-back earned a yellow card after squaring up to the veteran striker.
West Ham sought to exploit the home side's indiscipline and went close on 25 minutes when Ian Walker diverted a Marlon Harewood shot into the path of Matthew Etherington, who shot narrowly wide from eight yards.
After the break Walker again saved Leicester when he dived to block a Harewood shot and then scrambled across his goal to prevent Teddy Sheringham sweeping the loose ball home.
David Connolly was denied on the hour mark by the brilliant one-handed save by Stephen Bywater.
Then on 70 minutes Connolly almost scored against his old club with an 18-yard effort which flew narrowly wide.
West Ham were themselves reduced to ten men five minutes from the end when Brevett was shown a second yellow card for a two-footed tackle on James Scowcroft.
Then deep in stoppage time West Ham squandered a great chance to nick it, as Bobby Zamora headed over from close range with just the keeper to beat.