Leicester came out of the blocks quickly and Gareth Williams forced Palace goalkeeper Gabor Kiraly into a save in just the second minute with a swerving drive from the edge of the box.
Moments later the Hungary international was forced to turn aside Johannes Gudjonsson's 20-yard shot for a corner which was cleared.
City continued to monopolise possession and Kiraly was called into action again on 15 minutes when he got his body behind a long-range shot from Hughes.
Palace had to wait until the 20th minute for their first serious threat, when Ben Watson fired an Andy Johnson knock down straight at home keeper Paul Henderson.
Henderson was sharply off his line to deny Johnson seven minutes later and then had to turn away an angled drive from Michael Hughes, as Palace turned up the pressure.
However, it was Leicester who grabbed the lead three minutes before half-time.
Williams robbed Darren Ward and then, with a clever back-heel, found Iain Hume whose angled shot was blocked, but from the rebound he found Welsh at the back post and the winger side-footed into the roof of the net.
Five minutes after the break Watson tried his luck from distance and forced Henderson into a diving save.
Then City threatened twice on the hour mark. First Gudjonsson's 22-yard shot fizzed just wide of an upright and then Fryatt drove wide from a tight angle after good work from Hume.
Alan Maybury came to the Foxes' rescue on 64 minutes when his last-ditch block diverted Jobi McAnuff's goal-bound shot for a corner.
Much of the pleasing passing that had been evident from both teams disappeared as the game wore on, with City forced increasingly into their defensive shell as Palace fought desperately for a leveller.
But it was Leicester who put the result beyond doubt with three minutes remaining after the skilful Fryatt comprehensively beat Gary Borrowdale to create the space to square for Hughes, who swept the ball home from 12 yards out.