London Road was packed with more than 13,000 fans for the clash between the local rivals but the home supporters had little to cheer as the Canaries dominated despite making eight changes to the side beaten by West Ham on Tuesday.
Elliott Bennett opened the scoring in the 30th minute and Simeon Jackson added a second four minutes before half-time.
The expected challenge from Posh never really materialised, with the excellent Robert Snodgrass grabbing a third in the 70th minute and Declan Rudd's only save coming in the final minutes of the match.
Hughton said: "Our approach to the game was very good, very professional from the first minute, but of course you need to score goals to give yourself a bit more of a comfortable time.
"I think probably the pivotal time was at half-time because if they get a goal back then it could be a tough afternoon but I thought we were very professional from first to last minute."
Snodgrass, one of only three players retained from the loss to West Ham, was the star of the show, setting up the first goal before applying a clinical finish to a second-half break.
Hughton added: "He's a good player. I made the decision to make some changes. Robert's one that I know can play games, he's a fit lad. I think he just showed the form that he's been showing for us.
"He's been playing consistently and has been adding some goals to his game and assists. But I thought he was part of a really good all-round team performance."
- Sports & Recreation
- Robert Snodgrass
- Elliott Bennett