Liverpool kept pace with the Premier League's leading pack as Mohamed Salah's 100th English top-flight goal helped them to victory at Leeds.
The game was somewhat marred, though, by a dislocated ankle to teenage midfielder Harvey Elliott, who was stretchered off following an initially innocuous-looking sliding challenge from Pascal Struijk that ultimately saw the Leeds player sent off.
Liverpool were already firmly in control of the game by then, though.
Egyptian forward Salah was perfectly placed to tap in Trent Alexander-Arnold's low cross and give the Reds a 20th-minute advantage, with Fabinho bundling home the second following a corner five minutes after the break.
Sadio Mane had missed a number of chances in the game, but made absolutely certain of the points with a low finish into the far bottom corner in injury time.
Leeds had their chances too, with Rodrigo firing the best of them straight at Alisson with the game still goalless.
But with a man fewer, Leeds could not muster the challenge required and have now failed to win any of their first four top-flight matches in a season for the first time since 1958-59.
They will also now have to deal with a shortage of numbers in central defence, with Struijk banned and Diego Llorente limping off in the first half to join Robin Koch on the treatment table.
Jurgen Klopp's side move to 10 points, level at the top, but with a lower number of goals scored than Manchester United and equal with Chelsea.
They have extended the division's longest unbeaten run to 14 and won eight of their last nine away games, including each of the previous five.
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Salah shines as Liverpool show their quality
This fixture has provided many quality moments for the English top-flight showreel down the years - a series of fiercely-contested matches in the 1960s and 70s, the Reds winning a 5-4 epic in 1991, Tony Yeboah's thunderous volley and Mark Viduka netting four goals 21 years ago.
There is always an edge, a feisty atmosphere fashioned by the visit of one of English football's elite to the home of a side with a proud history of their own - and aspirations to add to it.
These are the games Elland Road has most missed in the 16 years Leeds spent outside the Premier League and last season's fan-free affair. This was fittingly played out to a vibrant and hostile wall of noise.
The game itself delivered too, complete with another scoring feat as Salah notched his 100th Premier League goal via a simple finish.
Only Alan Shearer (124), Harry Kane (141), Sergio Aguero (147) and Thierry Henry (160) needed fewer Premier League appearances than the 161 it has taken him to reach the milestone.
Salah, Mane and Diogo Jota led the Leeds defence a merry dance throughout, threatening to run riot in a fascinating encounter packed with as many glaring misses as gloriously intricate attacking play, largely from the away side.
Rodrigo's failure to convert from 15 yards was bad, but Mane's scoop over the bar from point-blank range at 1-0 was the pick of a woeful bunch of finishes.
Fabinho's effort gave Liverpool complete control, but their immediate quest for further goals was undermined by the injury to Elliott, with the gravity of the situation quickly becoming apparent after Struijk had slid in to win the ball.
Referee Craig Pawson initially let play continue, but once it had stopped and medical assistance quickly called for the Reds player, a red card was shown on the hour to the United player.
Patrick Bamford did go close to giving the 10 men of Leeds hope with a stunning strike from halfway that Alisson had to tip over, but the game was well beyond Leeds by the time Mane claimed the visitors' third.
Player of the match
Mohamed SalahMohamed Salah
with an average of 8.38
Squad number23Player namePhillips
Squad number9Player nameBamford
Squad number10Player nameRaphinha
Squad number1Player nameMeslier
Squad number15Player nameDallas
Squad number2Player nameAyling
Squad number20Player nameJames
Squad number22Player nameHarrison
Squad number14Player nameLlorente
Squad number3Player nameFirpo
Squad number19Player nameRodrigo
Squad number6Player nameCooper
Squad number11Player nameRoberts
Squad number21Player nameStruijk
Squad number11Player nameMohamed Salah
Squad number67Player nameElliott
Squad number3Player nameFabinho
Squad number4Player namevan Dijk
Squad number66Player nameAlexander-Arnold
Squad number6Player nameThiago Alcántara
Squad number1Player nameAlisson
Squad number32Player nameMatip
Squad number26Player nameRobertson
Squad number10Player nameMané
Squad number20Player nameDiogo Jota
Squad number14Player nameHenderson
Squad number8Player nameKeïta
Squad number15Player nameOxlade-Chamberlain
- 14LlorenteBooked at 30minsSubstituted forStruijkat 33'minutesBooked at 60mins
- 6CooperBooked at 12mins
- 19RodrigoSubstituted forRobertsat 45'minutes
- 22HarrisonSubstituted forJamesat 68'minutes
- 4van Dijk
- 67ElliottSubstituted forHendersonat 63'minutes
- 3FabinhoBooked at 16mins
- 6Thiago AlcántaraSubstituted forKeïtaat 90+3'minutes
- 20JotaSubstituted forOxlade-Chamberlainat 82'minutes
Match ends, Leeds United 0, Liverpool 3.
Second Half ends, Leeds United 0, Liverpool 3.
Fabinho (Liverpool) wins a free kick in the defensive half.
Foul by Raphinha (Leeds United).
Attempt missed. Trent Alexander-Arnold (Liverpool) left footed shot from more than 35 yards misses to the right.
Attempt blocked. Fabinho (Liverpool) header from the centre of the box is blocked. Assisted by Andrew Robertson with a cross.
Corner, Liverpool. Conceded by Raphinha.
Substitution, Liverpool. Naby Keïta replaces Thiago.
Goal! Leeds United 0, Liverpool 3. Sadio Mané (Liverpool) right footed shot from the centre of the box to the bottom right corner. Assisted by Thiago.
Corner, Liverpool. Conceded by Junior Firpo.
Attempt blocked. Joel Matip (Liverpool) header from the centre of the box is blocked. Assisted by Trent Alexander-Arnold with a cross.
Corner, Liverpool. Conceded by Luke Ayling.
Attempt blocked. Sadio Mané (Liverpool) right footed shot from the centre of the box is blocked. Assisted by Jordan Henderson.
Offside, Liverpool. Jordan Henderson tries a through ball, but Sadio Mané is caught offside.
Hand ball by Jordan Henderson (Liverpool).
Offside, Liverpool. Sadio Mané tries a through ball, but Alex Oxlade-Chamberlain is caught offside.
Offside, Leeds United. Junior Firpo tries a through ball, but Raphinha is caught offside.
Corner, Leeds United. Conceded by Alisson.
Attempt saved. Patrick Bamford (Leeds United) left footed shot from more than 35 yards is saved in the top centre of the goal.
Foul by Fabinho (Liverpool).
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