BRISTOL ROVERS 0, UNITED 4 (Beckford 9, 65, Vokes 55, Kandol 87)
Bristol Rovers: Andersen, Regan, Elliott, Anthony, Lescott, Williams (Reece 84), Blizzard (Wright 72), Campbell, Hughes, Kuffour, Dixon (Duffy 72). Subs: Evans, Clough, Swallow, Richards.
United: Ankergren, Bromby, Naylor, Kisnorbo, Hughes, Snodgrass, Doyle (Kilkenny 73), Howson, Johnson, Beckford (Gradel 76), Vokes (Kandol 80). Subs: Crowe, Prutton, Michalik, Martin.
Referee: A Woolmer
Booked: Elliott (Rovers), Johnson, Doyle (Leeds)
Att: 11,448 (1640 Leeds)
Extended highlights and reaction available on LUTV...
United manager Simon Grayson named an unchanged team as he sought a response from his charges after a first league defeat of the season at Millwall the previous weekend.
The Memorial Stadium was packed to the rafters, and those home fans were voicing their disapproval within the first two minutes when Steve Elliott sent a goalbound Jermaine Beckford sprawling. The Rovers man escaped with a yellow card.
Robert Snodgrass, who scored a stunning free-kick here last season, saw his set-piece blocked and as Rovers scrambled the ball clear, play was held up again while Aaron Lescott received treatment.
But there were no interruptions after eight minutes when a superb passage of play saw United take the lead. Micky Doyle fed Beckford with an incisive pass and the United striker showed a cool head to convert.
Beckford came within a whisker of adding a second goal less than 60 seconds later. He rounded Rovers goalkeeper Mikkel Andersen while in pursuit out wide, but such was the tight angle and the distance, that his shot curled into the side-netting.
It was a lively opening and there was more of a zip about United's early play than at Millwall on Saturday. The passing was crisper and more fluent, and United clearly had more of an edge.
But there was a major scare for Leeds on 22 minutes when Stuart Campbell's shot from distance, the home side's first of the night, caught out Casper Ankergren and a fumble led to the woodwork rescuing United.
The Rovers players claimed the ball had crossed the line, but referee Andy Woolmer waved play on.
The opportunity gave the home side a lift, and they started to look livelier and enjoy their first real spell of pressure, but it was Leeds who went close again shortly after the half-hour when Sam Vokes fired just wide of the mark.
As the game headed towards half-time, the challenges were flying in with Jeff Hughes being felled by Doyle after an earlier spat with Snodgrass.
There had been little in the way of chances for either side, but Snodgrass did send one effort flying over the top on 44 minutes. And in the first minute of stoppage time, a near grounded Beckford was unable to make a connection when Andersen missed a ball forward from deep.
The second half started with Leeds on the front foot, looking to add to the single goal advantage, and it took some good defending by Hughes when Beckford lifted a ball into the box. Andersen saved the resultant corner when Vokes was waiting to pounce.
Beckford also steered an effort wide on 53 minutes after latching onto a ball over the top.
The second goal did come moments later though. Snodgrass played a lovely one-two with Beckford on the edge of box, and Vokes was on hand to sweep the cross home from close range to net his first goal in a Leeds shirt.
Moments later, Byron Anthony reacted well to clear the danger when Vokes sent in a low cross as Leeds threatened again, and Snodgrass curled an effort over the bar after Andersen had parried a low drive from Jonny Howson.
But Bristol Rovers, who had found themselves stifled by hard work and solid defending when needed, did skim the bar with a Hughes free-kick in reply.
United were superior, though, and it appeared to be game over in the 65th minute when Howson found Beckford, and the striker converted with aplomb at the far post to make it 3-0.
It was turning into United's most complete away performance so far this season. Leeds had passed and moved well, looked strong in the tackle, and restricted Bristol Rovers to little in the way of serious chances during the opening 70 minutes.
United also turned defence into attack quickly and a Bristol Rovers corner was followed by a sweeping move which saw Howson feed Beckford with a terrific pass allowing the striker, sniffing a possible hat-trick, to try his luck at curling a shot beyond the reach of Andersen.
While Beckford's shot went narrowly wide, Andersen was called upon to save a Bradley Johnson effort from distance, turning the striker around the post.
The home side came close to snatching a consolation as the game headed into the final 10 minutes, Andy Williams rounded off a good solo run by firing wide of the mark.
Grayson had made three changes by the 80th minute - handing run-outs to Tresor Kandol, Neil Kilkenny, and Max Gradel for the closing stages of the contest.
Leeds were in a real position of comfort and the home fans were streaming for the exits long before the whistle, having witnessed what was probably one of the best all-round performances they had seen from a visiting team for a good while.
Still Leeds pressed, though, and after Gradel was denied by the legs of Andersen in the 86th minute, the loan man supplied the the fourth goal of the night, for Kandol, 60 seconds later.
Gradel sent in a low cross from the byline and Kandol tucked the ball home from close range.
It was a fitting way to end what had been a comprehensive victory as United moved five points clear in the promotion places.