Leicester laid siege to the Bluebirds' goal in the first half with chance after chance going begging.
David Marshall made a handful of saves to keep the Foxes at bay and, when he was beaten by Andy King's long-range effort, a post came to his rescue.
Craig Bellamy looked a threat on the counter-attack throughout and it was he who grabbed the only goal of the game against the run of play after 25 minutes.
The Wales international showed great technique after collecting Craig Conway's pass to find the bottom left-hand corner of the net from 12 yards.
That seemed to knock the stuffing out of Leicester, who created very little afterward.