The Canaries were on a four-match losing streak while Posh had turned their Championship form around with a great run over the festive period, but it was straightforward for Norwich from the moment Elliott Bennett opened the scoring after half an hour.
Simeon Jackson doubled the lead four minutes before the break and influential midfielder Robert Snodgrass made sure with a third in the 70th minute.
Posh began brightly and Joe Newell may well have scored had Ryan Bennett not deflected his shot just past the post.
But their dominance was short-lived and Snodgrass was the main player as Norwich began to get on top. He did brilliantly to get his head to an overhit cross by Elliott Bennett in the 12th minute and Bobby Olejnik was at full strength to prevent the ball reaching Jackson.
The hosts' resistance was broken in the 30th minute with Snodgrass jinking into the area and setting up Elliott Bennett, who poked his shot into the bottom corner.
Posh manager Darren Ferguson made a tactical change, bringing on 17-year-old Jaanai Gordon for Craig Alcock and going to five at the back, but in the 41st minute they conceded again. A long ball from David Fox caught out the home defence and Jackson took his chance expertly with a cool lob over Olejnik.
And it would have been 3-0 at half-time but for the keeper, who stuck out a hand to divert Snodgrass' free-kick over the bar.
The most likely scenario appeared to be a third for Norwich, and Bradley Johnson came close but his 25-yarder was just wide while Jackson's header from a corner was blocked.
There were belated signs of improvement from Posh midway through the half but the game was all over in the 70th minute as Norwich broke away, Elliott Bennett fed Snodgrass and he calmly beat Olejnik.