Papiss Cisse's sublime first-half finish sunk Norwich as Newcastle secured a first win in five and revived their push for a European place.
Cisse superbly turned Jonas Gutierrez's cross into the top corner from 12 yards with the outside of his foot.
Cisse and strike partner Demba Ba were then denied by excellent John Ruddy saves as the Magpies dominated.
Victory was essential - Pardew
Norwich rallied after the break but Tim Krul tipped over a Zak Whitbread header and thwarted Anthony Pilkington.
It was an important return to winning ways for Newcastle, who had stuttered in recent weeks and seen their unlikely challenge for a Champions League spot fade away.
Boss Alan Pardew, in the 500th league game of his managerial career, had targeted five wins from Newcastle's remaining 10 games to seal a Europa League spot.
To that end, he recalled Cisse to the starting line-up after resting the £10m striker for the
bitterly narrow defeat by Arsenal in midweek.
And the Senegalese marksman produced a top-drawer strike to give the Tynesiders an early lead.
Gutierrez broke down the left and fired a bouncing cross into the danger area, where Cisse got ahead of defender Whitbread and brilliantly diverted a vicious shot past Ruddy.
DID YOU KNOW?
Norwich have conceded in 29 consecutive top flight away games - a Premier League record.
The goal set an unwanted record for City, who become the first team in Premier League history to concede in 29 successive away games.
They were soon gifted a chance to equalise by Newcastle defender Mike Williamson, whose dithering allowed Jonny Howson a clear sight of goal but the midfielder fired over.
The visitors had greater difficulty fashioning their own opportunities, and they were indebted to Ruddy for keeping them in the match.
First, the goalkeeper produced a stunning fingertip save to divert Ba's acrobatic volley inches wide.
He then rushed out to foil Cisse, who had been sent through by Gutierrez's pass.
'Excellent' Norwich please Lambert
There was a role reversal after the break as Ruddy's opposite number Krul was called upon to make two outstanding saves of his own.
The Dutch keeper turned Pilkington's shot wide, then made an even better save to tip Whitbread's header over the bar following a superb cross from Elliott Bennett.
The Canaries continued to pin back a suddenly tentative Newcastle side but the Mapgies defended diligently.
The closest Norwich came to levelling was in the last minute, when Steve Morison raced through one-on-one but stabbed his shot harmlessly wide.
When these sides last met in December, Norwich scored four goals from five shots on target as they completed a 4-2 win at Carrow Road.
This time around they had the same amount of shots but nothing to show for it, and Paul Lambert's side are now winless in five - although the manager can take heart from their second-half display.
For Pardew, it was a perfect 500th game and by his reckoning, his side are now just four wins away from Europe.
Newcastle manager Alan Pardew:
"We needed a win and we had an injury crisis. We weren't firing on all cylinders, had eight players injured and had to grind it out.
"We have finishers on the pitch and that helps. Cisse showed what he's about today, he could have had a hat-trick.
"We have now reset our goals and we're going for the Europa League."
Norwich manager Paul Lambert:
"We're disappointed to lose but I think the performance was excellent.
"This is a tough place to play, we switched off for the goal and have to defend better.
"But if we keep playing like that we'll be right up there. I have nothing but praise for the team."
Newcastle United 26 Krul 02 Coloccini 05 Simpson 06 Williamson 14 Perch 04 Cabaye 08 Guthrie (Gosling - 76' ) 10 Ben Arfa (Santon - 63' ) 18 Gutierrez 09 Cisse (Sh Ameobi - 69' ) 19 Ba Substitutes 35 Elliot 03 Santon 13 Abeid 15 Gosling 29 Vuckic 32 Donaldson 23 Sh Ameobi Norwich City 01 Ruddy 03 Drury (Hoolahan - 82' ) 06 Whitbread Booked 22 Ward 25 Naughton Booked 11 Surman 12 Pilkington (R Martin - 85' ) 15 Fox 17 E Bennett Booked 24 Howson (Holt - 77' ) 05 Morison Substitutes 31 Steer 02 R Martin 04 Johnson 07 Crofts 14 Hoolahan 09 Holt 10 Jackson