Jamie Vardy and then Harvey Barnes netted as the visitors refused to give in after Michail Antonio and Lucas Perez twice put the Hammers ahead.
The two mid-table sides both began in the unusual position of having equalled their points total of last season despite campaigns which promised more than they delivered.
Antonio opened the scoring with a superb bullet header from Mark Noble's cross in the 37th minute, with Vardy countering with a brilliant finish for his 16th goal of the season.
Substitute Perez thought he had won it on 82 minutes with a tap-in after fellow substitute Pedro Obiang had hit the post. He should have had another goal soon after but his effort was wrongly ruled offside by the linesman.
That allowed Leicester to launch one more attack and substitute Barnes kept his cool in injury time to slot home calmly for his first ever goal for the Foxes.
"I think we deserved more than a draw," said West Ham manager Manuel Pellegrini. "We should have been leading 3-1 but it was a mistake of the linesman. I've seen the goal again and he was one metre onside."
Leicester manager Brendan Rodgers also accepted West Ham's goal should have stood, saying: "It looks like we got away with one."
(Reporting by Neil Robinson; editing by Clare Fallon)
