After a goalless first half which saw Joelinton go off injured and Jonjo Shelvey force a smart save from Leeds goalkeeper Illan Meslier, the Magpies number 8 found the breakthrough with 15 minutes of normal time remaining from a free-kick.
The win leaves Newcastle 18th, just a point from safety with a game in hand on 17th placed Norwich City.
Their next Premier League match will be against Everton on February 9. The managerless Toffees sit just four points ahead of Newcastle in the table.
Eddie Howe made just one change from the previous match as Joe Willock came into the side for Sean Longstaff while Javier Manquillo returned from suspension with a place on the bench.
Here are Dominic Scurr’s player ratings from the match…
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1. LEEDS, ENGLAND - JANUARY 22: Allan Saint-Maximin of Newcastle United is challenged by Luke Ayling of Leeds United during the Premier League match between Leeds United and Newcastle United at Elland Road on January 22, 2022 in Leeds, England. (Photo by Stu Forster/Getty Images)
Allan Saint-Maximin of Newcastle United is challenged by Luke Ayling of Leeds United during the Premier League match between Leeds United and Newcastle United at Elland Road on January 22, 2022 in Leeds, England. (Photo by Stu Forster/Getty Images)
Photo: Stu Forster
2. Martin Dubravka - 7
Made a good save early on to deny Dan James and remained calm and collected throughout the game.
Photo: Shaun Botterill
3. Kieran Trippier - 7
Couldn't get forward as much as he would have liked as Leeds exposed Newcastle at the back in the first half but was much more of an outlet in the second. Made some important challenges.
Photo: PAUL ELLIS
4. Jamaal Lascelles - 6
Stepped forward and missed the ball in the build-up to Leeds' first decent chance which was saved by Dubravka. Recovered well after that and managed to keep Leeds at bay before limping off.
Photo: Stu Forster