The Magpies' French duo gave Alan Pardew's men a commanding first-half lead and, despite Leroy Fer's goal in the 80th minute, the Canaries could not muster a comeback.
The Frenchman put the hosts ahead inside two minutes, before compatriot Yoan Gouffran scored a second before the break. Leroy Fer pulled a goal back for the visitors 10 minutes from time, but it was too little too late for Chris Hughton's men.
Newcastle has now won three consecutive Premier League fixtures for the first time in 19 months, while Norwich has just one victory from its last six matches.
Alan Pardew made one change from the side that beat Tottenham Hotspur 1-0 prior to the international break, with Fabricio Coloccini — who has expressed his desire to leave the club — coming in for the suspended Mathieu Debuchy.
Former Newcastle boss Hughton, meanwhile, made two changes to the Norwich lineup that won 3-1 against West Ham last time out, with Bradley Johnson and Nathan Redmond replacing Robert Snodgrass and Johan Elmander.
It didn’t take long for the hosts to break the deadlock, as a second-minute Yohan Cabaye corner evaded the Norwich defense to find Remy lurking at the back post, and the Frenchman made no mistake in heading his eighth goal in as many appearances.
The visitors caused panic in the Newcastle defense after 13 minutes as an Anthony Pilkington free kick resulted in a goalmouth scramble, but Shola Ameobi was on hand to clear the danger.
Moussa Sissoko screwed an effort narrowly wide of the left post just after the half-hour, and Newcastle was almost made to pay for that wasted opportunity as a Pilkington header crept just wide of the target.
However, Gouffran doubled the home advantage seven minutes before the break when John Ruddy spilled an Ameobi header into the path of the winger, who prodded home the rebound for his third league goal of the season.
Ameobi drew a terrific diving save from Ruddy on the stroke of halftime from 25 yards, with the goalkeeper doing well to push the ball beyond his right-hand post and out for a corner.
Pilkington was forced off with a hamstring problem just after the restart, and the visitors continued to struggle to pose too much of a threat to Tim Krul’s goal. Newcastle switched to a more defensive approach in the second 45 minutes, rarely venturing too far into the Norwich half.
With goalscoring opportunities at a premium, Fer managed to get his head to a Martin Olsson cross in the 73rd minute, but sent his effort harmlessly over the crossbar.
However, Fer made amends seven minutes later, rising brilliantly to send a powerful header into the bottom right-hand corner of the net from 12 yards after Nathan Redmond corner's, but it proved a mere consolation for Norwich.