In the fifth minute of stoppage time, Ritchie De Laet forced Matt Ingram in the home goal to parry into the path of St Ledger who kept his cool to score from close range.
Jo Kuffour had earlier equalised for the home side after Dave Nugent had opened the scoring from the penalty spot in the first half for the Championship outfit.
Nugent tucked home the penalty after 14 minutes after Wycombe captain Stuart Lewis brought down Andy King in the area.
The hosts, who in 2001 famously beat Leicester in the FA Cup quarter-finals, almost equalised through Dean Morgan's left-footed drive before Kuffour turned on the edge of the box to rasp the ball home in the 21st minute.
Ingram pulled off superb stops from Neil Danns and Lloyd Dyer after the restart as the Foxes began to grow into the game.
After 68 minutes the visitors nearly found their breakthrough but Chris Wood fired wide, leaving St Ledger to spare their blushes late on.