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Leicester's strike duo of Leonardo Ulloa and Jamie Vardy linked up well in the 12th minute, but after Vardy collected a knock-down from his teammate, he saw his goalbound shot well saved by Julian Speroni.
David Nugent then found himself in front of goal unchallenged, but blazed his 20-yard shot over the bar.
After a shaky opening, the home side grew into the game and Palace's first meaningful shot of the first half came from captain Mile Jedinak in the 20th minute, but Kasper Schmeichel held on to the Australian's stinging strike.
Palace then peppered the Leicester goal with a series of shots. First, Damien Delaney saw his header cleared off the line by Esteban Cambiasso before Jason Puncheon was denied by Schmeichel. Frazer Campbell then nodded over the bar as the visitors breathed a sigh of relief.
Palace were certainly in the ascendancy and Yannick Bolasie teased Ritchie De Laet throughout the opening period and flashed a 36th-minute cross across the face of goal, but there was no-one there to meet it.