Swiss full-back Bruno Berner broke the deadlock after 68 minutes, Paul Gallacher curled home a delightful free-kick in the 79th minute and Andy King completed the scoring two minutes later.
Leicester consolidated fifth place in the table but a fourth successive away defeat saw Forest replaced by West Brom in second position.
Experienced midfielder Matt Oakley returned to the Leicester starting line-up after being left out of the squad at Doncaster in midweek.
His inclusion was one of two changes made by City manager Nigel Pearson who also recalled Gallacher. Nolberto Solano and Dany N'Guessan dropped down to the bench.
Forest fielded the same starting XI for the third straight game with boss Billy Davies keeping faith with the players that earned back-to-back home victories against Sheffield United and Middlesbrough.
Leicester started brightly and the lively Martyn Waghorn just cleared the crossbar with a 20-yard shot early on.
Forest responded through skipper Paul McKenna but the midfielder's long-range effort was easily fielded by Chris Weale.
The visitors began to assert themselves and Robert Earnshaw should have given Forest the lead on the half-hour mark when he was allowed a free header inside the six-yard box but the Wales international hit the crossbar.
A minute later, Earnshaw sent an acrobatic volley narrowly wide.
Forest resumed where they had left off in the first half after the break and Radoslaw Majewski stung Weale's palms with a 25-yard strike.
But Davies' side failed to take full advantage of their dominance and Berner put Leicester in front. Paul Gallacher had sent a warning shot across Forest's bow moments before when he fired over from the edge of the box.
Leicester were soon on the attack again and Richie Wellens controlled a ball on his chest on the edge of the area. He shaped to shoot but cleverly backheeled to Berner who blasted his shot beyond the helpless Lee Camp.
Another left-back, James Perch, should have equalised in the 77th minute but mis-hit his effort when well-placed in front of goal.
It proved a costly miss as two minutes later Gallacher curled a free-kick into the top corner.
Berner was involved again for the third goal, overlapping Lloyd Dyer down the left-hand side and sending in a driven cross for King to tap home from close range.
Substitute David McGoldrick almost conjured up a consolation goal for Forest in injury time but Weale tipped his effort around a post.