The Canaries move to within two points of second-placed Watford and never looked back after Jonny Howson had marked his 100th appearance for the club by firing them ahead on the stroke of half-time.
Cameron Jerome quickly made it 19 goals for the season with a cheeky back-heeled finish and it soon became 3-0 when Wes Hoolahan converted from the spot after Martin Olsson had been brought down.
Forest pulled one back from substitute Chris Burke 15 minutes from time but could have no complaints about a result that surely ends their outside hopes of making the play-offs.
Norwich had marginally the better of the keenly contested opening stages, with Bradley Johnson nodding a Howson cross wide while no-one could get on the end of Hoolahan’s clever cut-back.
Forest’s cause was not helped when they lost striker Dexter Blackstock to injury after just 17 minutes but they had plenty of the ball and gave the hosts a scare just after the substitution when Michail Antonio’s drive from a free-kick was blocked.
It was Norwich who were looking the more dangerous side though, with Hoolahan at the centre of most of their best moments, and they went close again midway through the half when Jerome’s powerful header into the ground went just over.
John Ruddy was quick off his line to foil Antonio at the other end as the match continued to ebb and flow, with Howson then narrowly off target with a flicked header from Steven Whittaker’s pin-point delivery.
Forest were gradually getting a foothold in the game and it took a smart reaction save from Ruddy to keep out Ben Osborn’s snap-shot after Antonio had caused havoc down the left.
Forest keeper Karl Darlow also did well to keep out a low skidder from Howson that was heading into the bottom corner before Norwich finally took the lead from the final move of the half. Hoolahan was the architect with a perfectly weighted through ball and Howson was coolness personified as he tucked the ball home.
The second period got off to a scrappy start but burst into life on 56 minutes when the Canaries doubled their advantage with a beautifully taken second goal.
The excellent Olsson set the chance up with a low cross from the left after a typically speedy dash from deep and Jerome conjured up a sublime back heel to divert the ball into the back of the net via the far post.
It was all Norwich now and they made it 3-0 from the penalty spot two minutes later when substitute Burke brought down the raiding Olsson in the box and Hoolahan blasted home from 12 yards.
Jerome later had an effort rightly ruled out for offside before Hoolahan curled the ball just wide after another flowing Norwich move.
Forest pulled one back on 75 minutes, with substitute Burke tucking away a loose ball from close range after Ruddy had failed to hold a long-range effort from Paterson.