After both sides had hit the woodwork in an evenly-contested first 45 minutes, the Foxes struck three times without reply after the restart to strengthen their grip on a play-off place.
The visitors, who began the match with 15 clean sheets so far this season, had not conceded more than a single goal since their 3-2 win over Derby County in August.
Lee Camp needed lengthy treatment after he was hurt defending Martyn Waghorn's early corner. Waghorn then accelerated beyond four Forest players before firing wide.
Forest's first threat arrived on ten minutes when Radoslaw Majewski hit a 20-yard drive which was comfortably saved by Chris Weale.
There was an opening for the home side when a Paul Gallagher cross fell to Bruno Berner at the far post but the full-back was unable to pick out a blue shirt.
Forest went close on 31 minutes when Majewski swung in a free-kick from the left and an unmarked Robert Earnshaw ghosted in to thud a header against the bar.
The visitors continued to probe while City too often resorted to the long ball forward.
The visitors were quickly on the offensive after the restart with Majewski testing Chris Weale from 20 yards.
City almost breached Forest's defensive on 54 minutes when Michael Morrison crashed a header against the bar from a Waghorn free-kick. Matty Oakley then teed up Gallagher whose angled shot flew over.
But Leicester's growing momentum was rewarded when they took the lead on 67 minutes. Forest struggled to clear a Gallagher free-kick which was turned in to the six-yard area by Richie Wellens where Berner was waiting to smash the ball into the roof of net.
Berner was then in the thick of the action at the other end when he blocked a goalbound shot by James Perch.
Confidence flowed through the home side who went two up on 79 minutes when Gallagher curled in a superb 19-yard free-kick over the defensive wall and into the top far corner of the net.
By now Leicester were lording it over their near neighbours and their superiority was rewarded with a third on 81 minutes when Lloyd Dyer fed Berner whose low shot was side-footed into the net by Andy King from 12 yards.