Emile Mpenza struck a glorious late goal to give struggling Manchester City a vital victory at St James' Park.
Mpenza has scored two goals in two games for City
Mpenza, who also hit the post with a fine 20-yard effort, lashed a shot past Given after a swift breakaway involving Joey Barton and Michael Johnson.
Newcastle, inspired by Scott Parker, looked dangerous in patches with Kieron Dyer and Damien Duff the main threat.
Steven Taylor saw a header hit the bar but Newcastle created precious few chances and were booed off at the end.
Glenn Roder's side began well enough with Dyer and Duff looking lively and Obafemi Martins posing problems to the City defence.
But despite dominating possession the home side only started to create decent chances in the final five minutes of an uninspiring match.
Taylor was unlucky to see a header come crashing back off the bar and Stephen Carr fired narrowly wide after a goalmouth scramble.
But most of the action was crammed into that frantic finale. City's packed midfield ensured their was little in the way of excitement in either penalty box for the first 75 minutes.
Dietmar Hamann and Barton countered the bite of Parker and Nicky Butt in central midfield and a goalless draw looked on the cards.
The best opportunity of an otherwise chanceless first period saw Mpenza fire a stunning shot on to the post from 20 yards.
And although there was plenty of passion and endeavour on the resumption, there was still little in the way of excitement.
Solano had a shot blocked after being teed up by Dyer and Parker's energy and drive from midfield was one of the few bright spots for the home side.
But it was a rare bit of quality from City that provided the game's telling moment.
Barton created space in the centre of the park and found Johnson whose clever pass allowed Mpenza to shoot across Shay Given.
City defended nervously for the final ten minutes but held on for a win that takes them onto 36 points and goes a long way towards ensuring their Premiership survival.
Newcastle manager Glenn Roeder:
"I understand the fans' frustration - I was very frustrated myself that we found it difficult to break them down.
"People do not realise how difficult it is playing against a team who get so many men behind the ball. When that happens, you must score that first goal to bring them out to play.
"They had once chance, the lad drove it home and that was it. They did not have another chance of any consequence. The few chances that came our way - and they were good chances - were after we went one down."
Manchester City boss Stuart Pearce:
"I said some months ago it is going to be very tight right to the end of the season, probably up until the last game.
"At the moment for me, any three teams from eight could be relegated, and we are one of the eight.
"I knew that at Christmas and I certainly know it now. We have some tough matches between now and the end of the season, but when you have to win matches, every game is a tough game, and that applies to any of the eight teams at the bottom of the table."
Newcastle: Given, Carr, Moore (Onyewu 73), Taylor, Babayaro, Solano (Milner 76), Butt, Parker, Duff, Dyer (Sibierski 77), Martins.
Subs Not Used: Harper, Emre.
Man City: Isaksson, Onuoha (Trabelsi 85), Dunne, Distin, Ball, Jihai, Barton, Hamann (Samaras 46), Johnson, Vassell, Mpenza.
Subs Not Used: Weaver, Corradi, Miller.
Booked: Vassell, Jihai, Barton.
Goals: Mpenza 80.
Ref: G Poll (Hertfordshire).