L Eicester is lifted temporarily and Vicente Iborra should have done better from six yards with a title rescued by Fabianski.
But the introduction of Vardy for the second half was inevitable, the bowl from home supporters might send a message to the boss.
It was a flurry of penalties for the home team – both waved away by Oliver – when James Maddison collided with Balbuena before Pablo Zabaleta seemed to handle a shot from Kelechi Iheanacho.
Fabianski also had an excellent evening driving away Marc Albrighton’s volley before he could easily claim the wings second effort.
Leicester was completely dominant now with Vardy wasting a chance with a bad headline in the nearest post after Albrighton’s brilliant cross. Harry Maguire then led a Maddison corner at the top of the upright.
West Ham’s defense swung between excellent and desperate; the ten men were subjected to pressure from all angles.
Puel took Demarai Gray and Shinji Okazaki in a bid to break West Ham’s resistance but it was remarkable that it was almost a second goal for the visitors.
Michail Antonio, a substitute, broke off halfway and recovered after losing the ball in the penalty area to shoot the corner but Kasper Schmeichel saved.