Sadio Mane is the third African player to score 100 Premier League goals after Didier Drogba and Liverpool team-mate Mohamed SalahRoberto Firmino scored a hat-trick as rampant Liverpool condemned Claudio Ranieri to a miserable start to life as Watford manager in a one-sided game at Vicarage Road.
The home side had no answer to Liverpool's fluid attacking play.
Sadio Mane became the third African player to score 100 Premier League goals before Roberto Firmino struck either side of the break and Mohamed Salah finished a brilliant individual goal with a smart shot beyond Ben Foster.
Salah's goal takes him level with former Chelsea striker Didier Drogba as the highest-scoring African player in Premier League history with 104 goals.
Firmino completed the scoring in the final minute for his first hat-trick since December 2018.
The result means Liverpool have scored three goals or more in all six away games in all competitions so far this season, something no other English top-flight side has ever managed. It also extended their unbeaten start to the season and took them back to the top of the table, before Chelsea's visit to Brentford (17:30 BST)
It could easily have been more but a combination of bad luck and - from Salah - a terrible mis-control cost them further opportunities.
Watford did not manage a corner until the 78th minute. That it was greeted with huge cheers and a standing ovation just about summed up Ranieri's day.
Ranieri's task laid bare
Watford is Ranieri's 22nd different job in his long and varied coaching career. Rarely can he have endured a start as sobering as this.
It was Watford's heaviest Premier League defeat since their eight-goal hammering by Manchester City in September 2019 and their biggest at home since the same opponents scored six here two years before that. There was certainly nothing to trigger a celebration before his 70th birthday on Thursday.
The dimensions of Vicarage Road mean the edge of the managers' technical areas are about as close as it is possible to get to the side of the pitch.
It meant that Ranieri was almost on top of the action as the size of his task was laid bare.
A long pre-match chat with Liverpool counterpart Jurgen Klopp was about as good as it got for the Italian.
The hosts simply did not get near enough to their talented opponents. Salah was given far too much space by Danny Rose even before he created the opener. Firmino was allowed to drop into the space between Watford's defence and midfield without anyone tracking his movements and Liverpool stroked the ball about at will further back, with no press to hurry them up.
With a paltry 17% possession, no shots, no corners and, obviously, no goals, the first half was a non-event for Ranieri and his new team. And if he hoped the introduction of Tom Cleverley into midfield for the second period would improve matters, he was sadly mistaken as Liverpool scored twice within 10 minutes of the restart.
Watford did rally towards the end, with Ismaila Sarr striking a post, although by then any chance of turning the game into a contest was long gone.
If there was a consolation for Ranieri, it is that there should be no dissenters if he wants to make significant changes during his first full week working with his new team.
However, with a fixture list that includes Everton, Arsenal, Chelsea and both Manchester clubs among Watford's next seven opponents, Ranieri needs a plan if his club's famously trigger-happy owners are not to be considering whether to axe yet another manager.
Rampant Reds
This was Liverpool's biggest win since the 7-0 hammering of Crystal Palace last December, which was also the last time Firmino, Salah and Mane all scored in a top-flight game.
In joining Egypt's Salah and Ivorian Didier Drogba as African goalscoring centurions, Senegalese Mane is part of a pretty exclusive Premier League club.
Salah's curling pass with the outside of his left foot could not have been any more inviting and Mane showed superb composure to meet the ball with perfect timing and give Foster no chance.
Firmino's three were welcome - but they were also all pretty straightforward. The first two were tap-ins thanks to James Milner's low cross into the six-yard area and the ball running loose from a desperate Ben Foster save after Craig Cathcart had turned the ball towards his own goal.
There was a bit more to the Brazilian's third as he ran forward with intelligence, something no defender countered, after Neco Williams had crossed.
But there was no doubting Salah's was the goal of the game.
Surrounded by three players on the edge of the Watford box, through a combination of speed, dexterity and brilliant close control, Salah got rid of them all before finding the target with his usual unerring accuracy.
It means he has now scored in eight successive matches in all competitions and in nine out of 10 in total, underlining why Liverpool are so keen for him to sign an extension to his current contract, which has less than two years to run.
Watford are next in action against Everton at Goodison Park on Saturday, 23 October (15:00 BST). Liverpool are at Atletico Madrid in the Champions League on Tuesday (20:00). Their next Premier League game is at Manchester United on Sunday, 24 October (16:30).
Player of the match
Roberto FirminoRoberto Firmino
Line-ups
Watford
Formation 4-4-2
1Foster
21Femenía15Cathcart5Troost-Ekong3Rose
25Dennis33Kucka19Sissoko11Masina
23Sarr29Hernández Suárez
1Foster21FemeníaSubstituted forNgakiaat 56'minutes15Cathcart5Troost-Ekong3Rose25DennisSubstituted forJoão Pedroat 69'minutes33Kucka19Sissoko11MasinaSubstituted forCleverleyat 45'minutes23Sarr29Hernández SuárezSubstitutes
2Ngakia6Louza8Cleverley10João Pedro12Sema16Gosling17Fletcher18Tufan26BachmannLiverpool
Formation 4-3-3
62Kelleher
66Alexander-Arnold32Matip4van Dijk26Robertson
7Milner14Henderson8Keïta
11Salah9Firmino10Mané
62Kelleher66Alexander-ArnoldSubstituted forOxlade-Chamberlainat 65'minutes32Matip4van Dijk26RobertsonSubstituted forTsimikasat 64'minutes7MilnerSubstituted forN Williamsat 83'minutes14Henderson8Keïta11Salah9Firmino10ManéSubstitutes
5Konaté12Gomez13Adrián15Oxlade-Chamberlain18Minamino20Jota21Tsimikas27Origi76N WilliamsReferee:Jonathan MossAttendance:21,085Live Text
Match ends, Watford 0, Liverpool 5.
Second Half ends, Watford 0, Liverpool 5.
Goal! Watford 0, Liverpool 5. Roberto Firmino (Liverpool) right footed shot from the left side of the six yard box to the centre of the goal. Assisted by Neco Williams.
Offside, Watford. João Pedro tries a through ball, but Ismaila Sarr is caught offside.
Sadio Mané (Liverpool) wins a free kick in the defensive half.
Foul by Jeremy Ngakia (Watford).
Attempt missed. Ismaila Sarr (Watford) header from the centre of the box misses to the left. Assisted by Jeremy Ngakia with a cross.
Offside, Watford. João Pedro tries a through ball, but Juraj Kucka is caught offside.
Attempt blocked. Cucho Hernández (Watford) right footed shot from the left side of the box is blocked. Assisted by Moussa Sissoko.
Offside, Watford. Ismaila Sarr tries a through ball, but João Pedro is caught offside.
Attempt saved. Ismaila Sarr (Watford) right footed shot from the centre of the box is saved in the bottom left corner. Assisted by João Pedro.
Substitution, Liverpool. Neco Williams replaces James Milner.
Foul by Konstantinos Tsimikas (Liverpool).
Juraj Kucka (Watford) wins a free kick in the defensive half.
Offside, Watford. Jeremy Ngakia tries a through ball, but João Pedro is caught offside.
Attempt saved. Sadio Mané (Liverpool) header from the centre of the box is saved in the top centre of the goal. Assisted by James Milner with a cross.
Attempt missed. Ismaila Sarr (Watford) right footed shot from the centre of the box is high and wide to the left following a corner.
Corner, Watford. Conceded by James Milner.
Foul by Naby Keïta (Liverpool).
Cucho Hernández (Watford) wins a free kick on the left wing.
