Loic Remy carried on his fine form by nodding in the opener after just two minutes, before Yoan Gouffran doubled Newcastle's advantage in the 38th minute after John Ruddy had spilled Shola Ameobi's header.
Leroy Fer powered in a fine header with ten minutes remaining to reduce Norwich's arrears and set up a nervous finale, but the Magpies held on to seal a third straight win.
Less than two minutes had gone when Yohan Cabaye, for the second time in the game, sent in a left-wing corner which was allowed to travel across Norwich's six-yard box to the far post.
Midfielder Bradley Johnson found himself caught in two minds and in the event did nothing to allow Remy to head into the back of the net.
The Canaries responded to the early setback to enjoy their best, albeit brief, spell of the half. Nathan Redmond perhaps should have done better after being played in over the top by Michael Turner with 11 minutes gone, but he blasted high over with the Magpies' defence waiting in vain for an offside flag.
The visitors went close once again two minutes later when Ryan Bennett turned Anthony Pilkington's deep free-kick towards goal to prompt a block by keeper Tim Krul, with returning skipper Fabricio Coloccini blocking Fer's follow-up and Ameobi mopping up.
However, with Cheick Tiote and Cabaye dominating in midfield, and Ameobi and Remy stretching the Norwich defence, Newcastle gradually established a momentum.
Moussa Sissoko should have extended their lead 14 minutes before the break after Ameobi had carved the City defence wide open with a slide-rule pass, but he dragged his effort wide.
Norwich were very nearly level within seconds when Pilkington looped a header back across goal, only for the ball to drop just wide with Krul wrong-footed.
However, Alan Pardew's men increased their advantage with 38 minutes gone when Ameobi once again produced a fine pass to pick out Remy, who fed Sissoko to float in a teasing cross.
Ameobi climbed highest to force a save from Ruddy, but Gouffran was on hand to tap home the rebound.
Ruddy had to dive to his left to beat away Ameobi's piledriver in stoppage time, and the home side headed for the dressing room happy with their lot.
The visitors' woes increased within four minutes of the restart when Pilkington was carried off after apparently damaging a hamstring in a challenge with Mapou Yanga-Mbiwa.
Johan Elmander took his place, but it was Gary Hooper who might have changed his side's fortunes from the resulting free-kick when Newcastle failed to clear their lines and he prodded a shot just wide.
Ameobi created a shooting chance for himself with some neat footwork, but then wasted all the good work by scuffing his attempt straight at Ruddy.
But Norwich were making a concerted push to get themselves back into the game and the Magpies found themselves having to defend, if with few scares, for an extended period.
Newcastle were content to try to hit the Canaries on the break, which they did to good effect on more than one occasion, but the precision of their first-half performance was sadly lacking.
The relative comfort of their position persuaded Pardew to withdraw the tiring Cabaye and Ameobi and replace them with Vurnon Anita and Papiss Cisse as time ran down.
However, Fer set up a tense conclusion when he headed Redmond's corner firmly past Krul with 10 minutes remaining, although the Magpies held firm.