A Demba Ba first-half strike proved the difference as Newcastle took the points at the Sports Direct Arena on a frustrating afternoon for the Canaries.
They scored with their first opportunity after the Canaries had created the early openings and possession, but it was down to the quality of the ball by Hatem Ben Arfa which found the Senegalese striker on 19 minutes to make it 1-0.
City will have been disappointed not to have got something out of the game with Andrew Surman and Robert Snodgrass both denied through a save from Steve Harper and a goal-line headed clearance by Mike Williamson.
Newcastle could have extended their lead having been awarded a penalty at the stroke of half-time - Steve Morison adjudged to have fouled Williamson in the box by referee Neil Swarbrick but thankfully Papiss Cisse's spot-kick blazed over the bar and although the Magpies created further opportunities City were in the game until the final whistle.
Hughton made two changes to his starting eleven from that which faced West Ham last weekend - noteably up front where Steve Morison came on for Grant Holt with Wes Hoolahan fitting in behind him in a 4-4-1-1 formation. Holt and Simeon Jackson were named on the bench with Anthony Pilkington who returned from injury having missed the Hammers match after failing a late fitness test.
Newcastle were still without goalkeeper Tim Krul through injury with veteran stopper Steve Harper between the sticks. Alan Pardew made several changes having rotated their squad for their Europa League match during the week. Cheick Tiote was named on the bench having missed Toon's previous six games.
City boss Chris Hughton received a warm welcome from the Newcastle faithful as he took his place in the dugout for the first time since his controversial sacking as Toon manager nearly two years ago.
On five minutes the Canaries created a good opportunity to take the lead when Javier Garrido found space on the left and delivered a good cross for Hoolahan to nip in only to see his header deflect just wide for a corner.
Three minutes later and the Canaries were dealt an early injury blow when former Newcastle defender Sebastien Bassong picked up a knock and had to be replaced by Michael Turner.
Twelve minutes in and City were showing some good movement and deliveries into the Newcastle box forcing the hosts to clear their lines.
Then on 19 minutes with their first shot on goal Newcastle took the lead - a delightful through ball by Ben Arfa found the run of Demba Ba who beat offside to slot the ball under John Ruddy for 1-0.
The hosts were now having more of the play with City forced to defend their area from more searching balls from Ben Arfa and Gutierrez.
However, the Canaries were still creating opportunities and on 27 minutes Robert Snodgrass was only denied by a goal-line clearance from Williamson.
Yohan Cabaye went close with a drive after latching onto the ball on the edge of the Norwich area after Papiss Cisse's inital miskick.
It was that final ball that was proving the difference for City with Hoolahan showing some good trickery to release Martin on the right but he couldn't get it past Steven Taylor - the Magpie defender conceding the corner.
Ben Arfa showed great quality again putting through a neat ball for Cisse - thankfully for City the Senegalese striker wasn't on his team-mates wave-length and the ball ran through for Ruddy to collect.
But on the stroke of half-time the hosts were given a great opportunity to make it 2-0 when Steve Morison was adjudged to have impeded Williamson in the box with a clumsy rather than menacing challenge and referee Neil Swarbrick awarded Newcastle a penalty kick. Cisse stepped up but blazed his effort high over the bar keeping it 1-0 going into the break.
Half-time: Newcastle United 1, Norwich City 0
Three minutes into the half and the Canaries had a great chance to equalise - after some good work by Hoolahan to control the ball he threaded through a pass for Surman who had made the run into the box, only to see his shot blocked by the onrushing Harper who kept his side in front.
The visitors were continuing to press and the foot of Gutierrez denied Snodgrass a clear shooting opportunity eight minutes into the half - his shot deflected for another corner.
On 56 minutes Ruddy had to be sharp to turn round the post Ben Arfa's long-range drive.
On the hour the Canaries broke through the middle but Johnson couldn't dig it out from under his feet and the Magpies managed to stop the move and break themselves, Cisse running into the area but could only finish with a tame shot, which Ruddy collected comfortably.
With 21 minutes left there were two changes - Cisse replaced with Gabriel Obertan and for City Grant Holt came on for Morison.
The Magpies made another change on 76 minutes Tiote coming on for Anita.
City's last substitution was in the form of Simeon Jackson replacing Surman for the last eight minutes.
Pressure from Leon Barnett and John Ruddy denied Ba a second goal after the Newcastle number 9 seemed through on goal.
Shola Ameobi also came on for the final few minutes with Ben Arfa coming off.
With two minutes left the Canaries received their first booking of the season for Jonny Howson's late challenge on Tiote. Which was swiftly followed by the Newcastle midfielder being booked himself for a challenge on Turner.
Newcastle managed to see out the four minutes of injury time to secure the points.
Final score: Newcastle United 1, Norwich City 0
NEWCASTLE: Harper, Santon, Cabaye, Williamson, Anita (Tiote 76), Cisse (Obertan 69), Ben Arfa (Shola Ameobi 85), Perch, Gutierrez, Ba, Taylor. Subs not used: Elliot, Bigirimana, Sammy Ameobi,
CITY: Ruddy, R. Martin (c), Johnson, Bassong (Turner 8), Snodgrass, Howson, Surman (Jackson 82), Hoolahan, Morison (Holt 69), Garrido, Barnett. Subs not used: Bunn, Pilkington, R. Bennett, Tettey.