Riyad Mahrez scored the only goal of the game after 34 minutes, finishing from Jamie Vardy's low cross.
The Foxes were on the back foot for much of the second half but they held out as Kasper Schmeichel saved from Bakary Sako and Damien Delaney volleyed against the crossbar in injury-time.
Leicester City will be aiming to move eight points clear of second-placed Tottenham when they face a Crystal Palace side who are yet to win in 2016.
Monday's 1-0 win over Newcastle ensured the Foxes will go into the international break as league leaders and they need 20 points to mathematically secure the title.
Claudio Ranieri's side currently have a five-point lead ahead of the trip to Selhurst Park and they will be confident of coming away with maximum points.
Crystal Palace have dropped from sixth in December to 15th and have lost their last five top-flight home games, but Alan Pardew will be hoping his side avoid equalling their longest losing run at home in Premier League history by derailing the visitors' title challenge.
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