Martin Olsson scored in stoppage time to earn Norwich a vital 3-2 win over a Newcastle side now staring at Premier League relegation.
Aleksandar Mitrovic's penalty four minutes from time had looked like rescuing a point for the Magpies to keep them three points behind their hosts.
But Olsson's precision finish leaves Rafael Benitez's side six points adrift of safety with seven games remaining.
The Canaries, who can further boost their survival bid against relegation rivals Crystal Palace and Sunderland in the next two weeks, appeared to have thrown victory away.
Mitrovic came off the bench to cancel out Timm Klose's first Norwich goal.
Dieumerci Mbokani scored three minutes later to restore the hosts' lead, but Mitrovic then converted from the spot after Gary O'Neil was penalised for handball
There was another twist to come as Olsson struck to earn Norwich back-to-back wins for the first time since the turn of the year, when they last won at home against Southampton.
Swansea took another step towards Premier League safety as they came back from two goals down to draw 2-2 at Stoke.
The Europe-chasing Potters looked destined for a fifth win in seven games after Ibrahim Afellay, on his 30th birthday, and Bojan Krkic had put them 2-0 up with goals in the 13th and 53rd minutes respectively
But Jakob Haugaard - in the Stoke goal as a replacement for the injured Jack Butland - was then beaten twice on his Barclays Premier League debut, by Gylfi Sigurdsson's strike in the 68th minute and then substitute Alberto Paloschi's deflected shot 11 minutes later.
The result sees 15th-placed Swansea remain 10 points clear of the relegation zone, while Stoke stay eighth after what they will certainly regard as two points dropped.
West Brom goalkeeper Ben Foster denied relegation-haunted Sunderland the victory they craved as a first clean sheet in 18 games for Sam Allardyce's side yielded just a single point.
Foster made important saves from Lee Cattermole, Jan Kirchhoff, two from Fabio Borini and another from Jermain Defoe at the death as the Black Cats made most of the running, but once again failed to profit from the opportunities they created.
Tony Pulis' side offered little going forward with home keeper Vito Mannone largely untroubled, but they left Wearside having reached the magic 40 points and having edged their hosts deeper into the mire following the 0-0 draw.
Sunderland went into the game having allowed four priceless points to slip from their grasp in away games at Southampton and Newcastle, where they led until the final few minutes, and knowing draws will not be enough to keep them in the top flight.
Dimitri Payet added another exquisite free-kick to his collection but Dwight Gayle dented West Ham's Champions League hopes by snatching a 2-2 draw for Crystal Palace.
Payet, fresh from stunning strikes at Manchester United and, for France, against Russia, conjured up another sublime set-piece at Upton Park.
But West Ham lost Cheikhou Kouyate to a straight red card before substitute Gayle's first Premier League goal of the season earned Palace a valuable point in their bid to steer clear of relegation trouble.
Damien Delaney had earlier given Palace the lead after a mistake by Hammers keeper Adrian, only for Manuel Lanzini to equalise.
Bakary Sako's 15th-minute free-kick from the right appeared to be curling out of play until, at the last moment, Adrian decided it might creep inside his far post.
But as the Spaniard attempted to gather the ball he inadvertently scooped it back into play, allowing Delaney to nod into an empty net.
Palace's lead lasted less than three minutes before Michail Antonio raided down the right and crossed to the back post.
Diafra Sakho's header back across goal was intercepted by Scott Dann, but cleared only as far as Lanzini who smashed it back past the defender and into the net.