After holding Leeds at bay for the majority of the league encounter, Jonjo Shelvey's low, curling free-kick from the edge of the penalty area opened the scoring in the closing stages of the second-half.
Eddie Howe's side, who suffered injuries to Joelinton, Paul Dummett and Jamaal Lascelles, then held firm to earn an important three points in their bid for Premier League survival.
Extending their unbeaten league to three matches, the victory saw Newcastle leapfrog relegation rivals Watford into 18th place on 15 points, lying one adrift of Norwich City with a game in hand over the Canaries.
Howe, making his 200th Premier League game as a manager, made one change to the side which claimed a 1-1 draw against Watford last week as midfielder Joe Willock, who completed a permanent move to Tyneside from Arsenal last summer, replaced Sean Longstaff.
Newcastle, who were targeting an eighth win out of their last 12 league trips to Elland Road, created the opening opportunity in front of goal as Joelinton controlled Joe Willock's pass inside the penalty area before the Brazilian's bending effort sailed wide of the target.
Goalkeeper Martin Dúbravka prevented Leeds' Dan James from breaking the deadlock in the early stages, denying the Welshman with an important one-handed save from close-range following Raphinha's dangerous cutback.
The hosts continued their push for an opener as Mateusz Klich's intended shot at goal flashed across the six-yard area before Raphinha fired an effort from the edge of the box over the crossbar minutes later.
Newcastle's sole shot on target during the opening 45 minutes almost resulted in a goal as Shelvey's volley from the edge of the penalty area was crucially pushed away by Leeds goalkeeper Illan Meslier.
In the second-half, James continued to cause problems for the Newcastle backline as the rapid winger darted in from the right wing before his teasing low cross flew past the penalty area.
Fabian Schär produced a crucial block to deny Jack Harrison from scoring as the winger, who netted in both league fixtures against the Magpies last term, raced into the box and after his goal bound effort hit the Swiss defender's heel, the loose ball fell to James but scuffed the follow-up.
After soaking up pressure from the Leeds attack, Newcastle pushed forward for a breakthrough as Sean Longstaff fired wide. After Ryan Fraser was unable to pick out Chris Wood, the striker was able to retrieve the loose ball before teeing up the North Shields-born midfielder but drove his effort wide of the left-hand post.
In the 75th minute, Newcastle found their breakthrough through Shelvey's free-kick. After substitute Javier Manquillo completed a mazy run down the left flank before being fouled by Diego Llorente on the edge of the box, Shelvey was on hand to convert the resulting set-piece, curling the ball into the bottom right-hand corner.
Newcastle aimed to double their advantage in the final minutes and were appealing for a penalty as Allan Saint-Maximin was tripped inside the box by Leeds defender Robin Koch but the decision was waved away by referee Chris Kavanagh along with VAR refusing to intervene.
Wood went close to registering his first goal in Newcastle colours as the New Zealand international advanced towards goal before the forward's deflected effort looped over the crossbar before Willock then saw a low strike saved by Meslier.
Despite five minutes of stoppage-time, Newcastle held off a late attacking surge from Marcelo Bielsa's Whites to secure their second clean sheet of the term along with a much-needed three points.
Newcastle United: Martin Dúbravka, Kieran Trippier, Jamaal Lascelles (c) (Ciaran Clark 69), Fabian Schär, Paul Dummett (Javier Manquillo 63), Jonjo Shelvey, Joe Willock, Joelinton (Sean Longstaff 42), Ryan Fraser, Allan Saint-Maximin, Chris Wood.
Subs not used: Karl Darlow, Jamal Lewis, Jeff Hendrick, Jacob Murphy, Miguel Almirón, Dwight Gayle.
