The Magpies held on despite a few close calls and move up to eighth thanks to a victory that consolidates their place in the top half of the table, while Norwich's woes away from home continue with an eighth defeat in their last 10 games on the road.
The match began in perfect style for the home side: a corner won with the opening move of the match was swung in by Yohan Cabaye, avoiding both the flailing arms of John Ruddy and the head of Bradley Johnson to find Loic Remy waiting unopposed to nod in from point blank range.
With Norwich having scored just three times all season away from home, the goal seemed a hammer blow early on - but Chris Hughton's men seemed determined to give a good account of themselves at their manager's former employed, and the visitors got back into the match.
Nathan Redmond and Anthony Pilkington both had good chances to equalise, but it was Newcastle who grabbed the second of the match with a finely-worked move. Shola Ameobi's perfectly-weighted pass released Remy up the right flan, and his floating ball found Ameobi in the box. The header was straight at Ruddy but powerful, and the England goalkeeper could not hang on - allowing Gouffran to tap in the loose ball.
Norwich's heads were already down, but fell further as Anthony Pilkington went off with a hamstring injury at the start of the second half, and with neither team making any headway an easy win seemed inevitable.
Chris Hughton's baffling reluctance to unleash his substitutes seemed to be backfiring until Fer headed home from the fourth of a series of late corners for the visitors.
That set up a frantic finale during which both teams had chances, but Newcastle hung on for a well-deserved third consecutive victory.
2' REMY OPENER: Remy opens the scoring thanks to terrible defending by Norwich: Bradley Johnson misses his clearing header on the line as the ball comes in from the corner, leaving Remy to nod home unopposed for the eighth and easiest goal of his stellar season so far.
11' GREAT CHANCE FOR NORWICH: Wonderful 40-yard ball from Michael Turner finds Nathan Redmond clear up front - he controls the ball perfectly as it drops onto his boot just in the box, but he blasts well over the bar. Big mistake not to find the target by Redmond - Norwich couldn't have asked for a much better opportunity.
30' SISSOKO BLOWS FANTASTIC CHANCE: Ameobi gets a perfectly-weighted pass through to Sissoko, who has only Ruddy to beat from inside the right side of the box. But he drags it wide! An appalling effort from Sissoko there, truth be told - Newcastle should be 2-0 up.
33' HUGE LET-OFF FOR NEWCASTLE: A hanging cross in from Redmond on the right finds Anthony Pilkington at the back post, who nods a looping header over Krul and seemingly towards the back post - but it goes just inches wide and Gary Hooper's header back towards the six-yard box is cleared by Mike Williamson.
38' GOUFFRAN MAKES IT 2-0: The Magpies in charge! Remy is released up the right by Ameobi and gets a wonderful ball in - where Ameobi has sprinted in and is waiting to head it. He does so, hits it straight at Ruddy who can only parry, and Gouffran is there to tap in from two yards.
46' PILKINGTON GOES DOWN: The first move of the second half sees Anthony Pilkington pull up sharply with what's clearly a hamstring pull - he'll be off momentarily. No coming back from that and he'll be lucky to play again this year.
71' AMEOBI INTO ORBIT: Jeers all around St James' Park! Great footwork from Ameobi sees him earn clear sight of goal just outside the box - but he scoops so far underneath it it's amazing he doesn't take a divot. He also falls onto his backside to complete his humiliation.
73' BEST CHANCE OF THE HALF: Norwich come close to an equaliser thanks to a great cross in from the left by Martin Olsson, who finds Leroy Fer... but the header skims just over the bar.
80' NORWICH BACK IN IT: Norwich win a fourth corner in quick succession and Redmond's ball is perfect for Leroy Fer: he nails his header perfectly and it clatters in off the right upright despite Krul getting a glove to it. Game on!
K - The row of seating reached by Loic Remy's appalling skied shot late in the first half. He laughed about it - but it's easy to chuckle when you're 2-0 up and already have your name on the scoresheet.
18 - The number of games since Shola Ameobi scored for Newcastle in the league, though he set up one goal and hit a volley that produced a world-class save from John Ruddy.
L - The row of seating reached by Loic Remy's appalling skied shot late in injury time which would have secured the match, despite Papiss Cisse being unmarked, in the box and just a few yards away from his team-mate. He didn't laugh after this one - and nor did Cisse.
TALKING POINT: Because they're worth it? Newcastle director of football Joe Kinnear revealed in the programme notes that all the club staff have gambled their entire annual bonuses on finishing in the top half. On this evidence that seems a canny decision.
MAN OF THE MATCH - Shola Ameobi (Newcastle): Set up one goal and only a world-class save from Ruddy prevented him from scoring with a superb volley. A creative threat throughout, and subbed off to a deserved ovation.
Newcastle: Krul 6; Yanga-Mbiwa 6, Coloccini 7, Williamson 7, Santon 7, Sissoko 7, Cabaye 7, Tiote 6, Gouffran 7, Shola Ameobi 8, Remy 7. Subs: Anita 6, Cisse 6.
Norwich: Ruddy 6, Martin 6, Turner 7, R Bennett 6, Olsson 7, Johnson 5, Fer 6, Howson 5, Redmond 7, Pilkington 6, Hooper 5. Subs: Elmander 6.
MATCH IN A TWEET