Chelsea ran riot in a 5-0 hammering of Everton the previous day to reach the summit, but Liverpool responded in kind with a slick, incisive display at Anfield to displace Antonio Conte's men.
Unsurprisingly it was Coutinho, Firmino and Mane that proved the Hornets' tormentors in chief and the latter met Coutinho's cross to open the scoring.
Coutinho drilled home from Firmino's pass to double the lead and there was a simple elegance about the third as Emre Can nodded in Adam Lallana's cross before half-time for his second goal in as many games.
Liverpool were equally impressive after the break. Lallana teed up Firmino to make it four and the Brazil international turned provider for Mane to score his second.
Daryl Janmaat grabbed a consolation for Watford, but Georginio Wijnaldum rounded off the rout in injury-time.
It was a huge statement of intent from Jurgen Klopp's men who are now unbeaten in nine top-flight games, while Watford - who had kept three straight clean sheets prior to the rout - must lick their wounds over the international break.
Liverpool were bright from the off and Firmino volleyed Lallana's cross at Heurelho Gomes before Lucas Leiva drove straight at the Watford goalkeeper from point-blank range.
The Reds continued to pour forward in numbers and Mane broke at pace to tee up Coutinho, who took a great touch inside before drilling wide of the near post.
Liverpool's football was scintillating and Firmino wastefully poked wide when slipped in by Coutinho.
The breakthrough finally arrived in the 27th minute, though. Coutinho worked a short corner with James Milner before delivering for Mane to glance his header past Gomes.
It was 2-0 three minutes later. A slick move led to Firmino picking out Coutinho, who took a touch out of his feet and drilled into the bottom-left corner from the edge of the box, Watford's misery compounded when Gomes limped off.
And the game was put beyond doubt shortly before the break. Lallana crossed from deep on the right and the unmarked Can guided a simple header past substitute keeper Costel Pantilimon.
There was no let-up after the interval and there was little surprise when Liverpool made it 4-0 in the 57th minute. The Reds carved open the visiting defence and Lallana's brilliant low ball was turned home by Firmino.
By the hour it was 5-0. This time Firmino slipped in a wonderful pass to Mane, who clinically finished past Pantilimon.
The game was well beyond Watford, but Etienne Capoue was twice denied by Loris Karius before their brief spell of pressure yielded a goal back when Janmaat coolly finished past Karius.
Liverpool remained in control, though, with substitute Daniel Sturridge twice rattling the crossbar, and it was from his saved shot that Wijnaldum turned in the rebound to get off the mark for the Reds.
