Newcastle spurned several chances but had too much for struggling Leeds.
Alan Shearer put Newcastle in front with an early goal, drilling the ball home with his right-foot from 16 yards.
Kieron Dyer then missed from short range, Paul Robinson saved a Jermaine Jenas drive and Shearer struck wide from 10 yards.
But Leeds rallied after the break, with Dominic Matteo shooting over, Mark Viduka forcing a save from Shay Given and Michael Bridges missing the target.
The result means Newcastle remain firmly in the hunt for a Champions League place, but Leeds stay anchored in the relegation zone.
Leeds went into the game without Alan Smith, who started his two-match ban after throwing a plastic bottle back into the crowd at the Carling Cup tie against Manchester United at Elland Road.
Newcastle, unchanged from the team that breezed past Southampton in the FA Cup, wasted little time in continuing their fine form.
Dyer, who scored twice against Saints, combined with Aaron Hughes and Nolberto Solano to tee-up Shearer, who beat Robinson for his 16th Premiership goal this season.
The home team continued to dominate and Dyer, playing in a forward role, should have doubled Newcastle's lead but missed the target from eight yards after neat work from Laurent Solano.
Jenas then forced a good save from Robinson with a superb long-range drive.
Leeds problems intensified when David Batty caught his studs in the turf and had to be substituted.
Jenas picked out Shearer with an exquisite pass shortly before the break, but the Newcastle striker missed the target from a good position.
4 mins: Shearer opens the scoring
20 mins: Robinson saves from Jenas
59 mins: Given saves Viduka's header
61 mins: Speed heads onto the woodwork
Leeds hinted after the break that they might punish Newcastle's failure to convert more of their chances.
Matteo drilled his shot over the crossbar after Viduka had dribbled into the Toon penalty area and cut the ball back into his skipper's path.
Viduka then failed to inject enough power into a floated cross from James Milner and Given comfortably saved.
Leeds Eddie Gray, sensing his team might snatch an unlikely point, introduced Bridges for Seth Johnson.
Bridges almost made an instant impression, but Titus Bramble made a crucial block.
Michael Duberry then had a shot charged down as Leeds pushed for a goal and Bridges again found himself in a good position, 10 yards from goal, but smashed his shot into the ground.
Despite Leeds pressure, Newcastle continued to look dangerous when in possession and Gary Speed powerfully headed a Robert corner from eight yards on to the outside of the post.
Substitute Hugo Viano almost beat Robinson from 30 yards, but Robinson tipped the shot around the post.
Newcastle: Given, Hughes, Woodgate, Bramble, Bernard,
Solano (Ambrose 81), Jenas, Speed, Robert (Viana 80), Shearer,
Subs Not Used: O'Brien, Harper, LuaLua.
Leeds: Robinson, Kelly, Duberry, Kilgallon, Harte, Pennant,
Matteo, Batty (Olembe 30), Johnson (Bridges 69),
Milner (Sakho 89), Viduka.
Subs Not Used: Carson, Richardson.
Referee: P Dowd (Stoke-on-Trent).