After dominating the opening 20 minutes, Newcastle took a 23rd-minute lead when Rob Green spilled a 40-yard lob from Jack Colback and Dwight Gayle poked the loose ball home from close range.
Leeds were then incensed when referee Graham Scott failed to award them a 43rd-minute penalty for handball and Newcastle doubled their lead nine minutes after the interval when Vurnon Anita and Ayoze Perez played a lovely one-two to feed Gayle who easily finished from close range.
Defeat leaved Leeds seventh but still only one point off the play-offs ahead of next Saturday’s trip to bottom of the table Rotherham United.
Classy Newcastle are now five points clear at the top of the division and look destined to win the Championship at a canter.
Amid a crescendo of noise and a wonderful atmosphere, Newcastle did all of the early pressing with the Magpies going close to taking a fifth minute lead.
A corner won by top scorer Gayle was laid back from Jonjo Shelvey to Vernon Anita whose low shot took a deflection and squirmed behind Green’s goal.
Then, two minutes later, Green had to be alert to rush off his line and clear a Shelvey free-kick that threatened to pick out Gayle.
Leeds were struggling to get out of their own half against the Championship leaders but the game then became secondary in the 11th minute when both sets of fans united for a rousing minute’s applause in memory of Gary Speed.
But Leeds were then back under the pump a few minutes later with Gayle showing lightning pace to almost burst through, before Charlie Taylor made a brave and important block to keep out a fierce drive from Matt Richie.
More Newcastle pressure then led to a 20th-minute low drive from Richie being saved by Green at his left-hand post.
United’s only forays both came through Taylor and Souleymane Doukara down the left flank with a 22nd-minute cross from Taylor floating over the bar.
But it was one-way traffic and no surprise when Newcastle took a 23rd-minute lead though with a goal that surely could have been prevented.
From near the centre circle, a Colback lob caught Green napping and the ‘keeper back-tracked on to his line before flapping the ball away but only to the feet of Gayle who tucked the ball home from close range.
Leeds attempted to rally as Chris Wood headed over but Newcastle very nearly doubled their lead in the 26th minute when Yoan Gouffran fired the ball just wide from the edge of the box.
But Leeds upped the ante around the half hour mark when a Kalvin Phillips free-kick found Luke Ayling whose header was clawed over the bar by ‘keeper Karl Darlow.
From the resulting corner, Pontus Jansson’s header was also saved by Darlow on his line.
Ronaldo Vieira then blazed over five minutes later as Leeds gradually got going and a lively Taylor then danced into the Magpies area and went tumbling down amidst flailing legs but referee Graham Scott was not interested in awarding a penalty.
Kemar Roofe’s shot was then deflected behind for a 40th-minute corner which was cleared.
But Leeds then won a series of corners to put Newcastle under huge pressure leading up to the interval with the Whites incensed when referee Scott waved away very strong claims for a penalty when a Vieira cross was blocked by Colback’s elbow.
A furious Jansson was booked for his protests and eventually Newcastle saw out the storm to half time.
There were no changes made during the half-time interval and four minutes after the restart Leeds went extremely close to equalising through Eunan O’Kane.
The midfielder wriggled free in the Magpies box and produced a low shot that was heading for the net until Darlow tipped the ball just wide.
And that save proved all the more crucial five minutes later when Newcastle doubled their lead as Gayle bagged his second of the afternoon.
There appeared little danger as Newcastle held possession on the right flank but Anita and Perez combined to produce a lovely one two that gave Anita space to produce a wonderful low cross that cut open United’s defence and Gayle was always going to score from just six yards out.
It already looked a case of game, set and match but Leeds attempted to rally and an effort from Ayling took a deflection before looping over.
Whites head coach Garry Monk then brought on Hadi Sacko for Vieira just after the hour and Doukara went close to playing in Roofe shortly after but overhit his pass.
Doukara again threatened with 17 minutes left when his header from ten yards forced Darlow to make another save.
Doukara then made way for Marcus Antonsson with 13 minutes left and Magpies boss Rafa Benitez then took off Gayle for Aleksandaer Mitrovic with the game already flattening out though Leeds went close with eight minutes left when Ayling’s cross just eluded Antonsson and then Wood.
Jansson was then perhaps lucky to avoid a second yellow card for a heavy tackle on Mitrovic but the game looked done.
One slightly nervous moment for Newcastle saw Darlow smash a clearance against Wood but the ball flew behind for a goal kick.
Leeds kept going but a wayward Ayling cross then sailed out of play in the 88th minute.
The Whites were then given three minutes of added time to try and salvage something but Newcastle were home and hosed and at this rate the same comment will soon apply in their quest to win the division.
Leeds United: Green, Ayling, Jansson, Bartley, Taylor, O’Kane, Vieira (Sacko 61), Doukara (Antonsson 77), Phillips, Roofe, Wood. Subs not used: Silvestri, Cooper, Berardi, Grimes, Dallas.
Newcastle United: Darlow, Anita, Lascelles, Clark, Dummett; Colback (Hayden 83), Shelvey; Ritchie, Gouffran (Diame 75), Perez; Gayle (Mitrovic 78). Subs not used: Sels, Yedlin, Mbemba, Atsu.
Referee: Graham Scott.