They might easily have been awarded at least one first-half penalty, but when Andy D'Urso did point to the spot 13 minutes from full-time, his decision was thought to be rather harsh on the Leicester team.
After Robert Earnshaw had given Norwich the lead with a well-timed run and cool finish, the Foxes drew level on 63 minutes when Gareth Williams fired in a cracking 25-yard drive.
Leon McKenzie calmly put away the Norwich penalty that denied the Foxes a point that many neutrals thought they deserved.
The visitors kicked off attacking the River End goal and probably had the better of the early exchanges.
The home fans showed some displeasure at their side's failure to play the ball on the ground in the windy conditions.
But in the 28th minute they directed their frustration at referee D'Urso when he failed to award a spot-kick after Gary Doherty was pushed as he attempted to head the ball towards the Leicester goal.
However, within seconds Norwich took the lead when Earnshaw took Youssef Safri's diagonal through ball in his stride and ran on to beat the advancing Paul Henderson with a low left-foot shot from 18 yards.
Andrew Hughes was only inches away from doubling the lead four minutes later when his snap-shot went wide after a good build up by Norwich.
Robert Green denied Matt Fryatt a scoring chance with some safe handling after 38 minutes.
The wind continued to frustrate the players as indicated by Darren Huckerby's shot which ballooned over the bar a minute from half-time.
Two minutes into the second half Green again did well to save Fryatt's low angled shot even though it may have gone wide.
On the hour Hughes was booked for halting Huckerby's run with a trip.
Doherty had a goal disallowed for alleged pushing before Williams stunned the home crowd with a spectacular right-foot 25-yard piledriver which beat Green to his right.
The leveller lifted the Foxes but they were undone when Richard Stearman was deemed to have fouled Huckerby as he burst into the box from the left wing.
In the aftermath Patrick McCarthy and Huckerby were both booked for speaking out of turn before McKenzie's spot-kick beat Henderson's despairing dive to his right to clinch victory for the hosts.