Foxes youngster Joe Dodoo, who scored a hat-trick in the previous round against Bury, scored just six minutes into his full debut taking advantage of Hammers defender James Collins' rustiness.
The game ebbed and flowed but Dodoo had another very good chance to make it 2-0, getting in behind again as Collins struggled with the pace of the game early on.
A frenetic first half burst into life on 26 minutes when Zarate, on his return to the team after a spell out through injury, pick up the ball 25 yards out and unleashed a left-footed drive.
It took a wicked deflection off a Leicester defender to wrong foot Mark Schwarzer in the hosts' goal and draw Slaven Bilic's side level.
Host of changes
There were a host of changes for both sides with Leicester's youthful exuberance countering the Hammers' experienced outfit well.
West Ham left back Aaron Cresswell had a free-kick saved after good work to draw a foul on the edge of the box by Victor Moses. Schwarzer fumbled but just gathered up the loose ball before Andy Carroll could get there.
Carroll and Collins then caused panic in the Leicester box from a corner as the Hammers really started to dominate late on it the half but it came to nothing.
And just before the break Claudio Ranieri's side could have found themselves 2-1 up when Dodoo's cushioned volley went wide of Adrian's post.
There looks certain to be more goals in this clash of the Premier League's top scorers with the potential for extra-time and penalties should they be needed.