French striker Emmanuel Riviere put Newcastle ahead in the 24th minute with his first league goal for the club on his 18th appearance.
Matt Phillips headed in Charlie Austin's cross for a 55th-minute equalizer and Leroy Fer scored from long range in the 61st for the winner.
Newcastle is two points clear of third-from-bottom Hull heading into next Sunday's home match against West Ham, which is coached by former Newcastle manager Sam Allardyce. Hull plays Manchester United at home and has a superior goal difference to Newcastle.
QPR was relegated last weekend.
Newcastle revival continues with victory at Burnley
Hull closer to relegation after 2-0 loss at Spurs
Meanwhile, Hull plunged closer to relegation from the Premier League by losing 2-0 to Tottenham after second-half goals by Nacer Chadli and Danny Rose on Saturday.
With one game left — at home to Manchester United next Sunday — Hull is third from bottom, two points behind Newcastle and three adrift of Sunderland.
Chadli rounded Hull goalkeeper Steve Harper to slot home in the 54th minute and left back Rose added a second with a powerful shot in the 61st.
Tottenham stayed sixth and kept the team in contention for Europa League qualification.
Hull's loss ensured Aston Villa and Leicester will be in the Premier League next season and reduced the fight to avoid relegation to three clubs. Burnley and Queens Park Rangers are already down.
Summaries Saturday from English football (home teams listed first):
English Premier League
Burnley 0, Stoke 0
Halftime: 0-0.
Liverpool 1, Crystal Palace 3
Liverpool: Adam Lallana (26).
Crystal Palace: Jason Puncheon (43), Wilfried Zaha (60), Glenn Murray (90).
Halftime: 1-1.
Queens Park Rangers 2, Newcastle 1
Queens Park Rangers: Matt Phillips (54), Leroy Fer (61).
Newcastle: Emmanuel Riviere (24).
Halftime: 0-1.
Southampton 6, Aston Villa 1
Southampton: Sadio Mane (13,14,16), Shane Long (26,38), Graziano Pelle (81).
Aston Villa: Christian Benteke (45).
Halftime: 5-1.
Sunderland 0, Leicester City 0
Halftime: 0-0.
Tottenham 2, Hull City 0
Tottenham: Nacer Chadli (54), Danny Rose (61).
Halftime: 0-0.
West Ham 1, Everton 2
West Ham: Stewart Downing (62).
Everton: Leon Osman (68), Romelu Lukaku (90).
Halftime: 0-0.
England Championship Playoffs
Norwich City 3, Ipswich 1
Norwich City: Wes Hoolahan (50, pen.), Nathan Redmond (64), Cameron Jerome (76).
Ipswich: Tommy Smith (60).
Halftime: 0-0.