Brendan Rodgers's men smashed Southampton 9-0 last Friday, but were made to work much harder for all three points by a resilient Palace.
Soyuncu's stooping header from James Maddison's corner just before the hour mark made the breakthrough and Vardy's hot streak continued when he finished off an excellent team move two minutes from time.
Leicester edge ahead of Chelsea on goal difference and six points clear of fifth-placed Arsenal, who they host next weekend, in the battle for a top four finish.
Vardy had the best opportunity of an uninspired first half when a wonderful Maddison pass freed the former England international in behind, but he could not force the ball beyond Vicente Guaita from a narrow angle.
Set-pieces seemed the most likely source of a goal for either side early on and Jonny Evans headed the first warning shot from the visitors looping just over moments later.