The Reds steamrollered Villarreal 3-0 on Friday (AEST) to book a UEFA Europa League final against Sevilla in Basel, and they continued their strong domestic home form against the Hornets on Monday (AEST).
The much-changed hosts took the lead deep in the first half when Allen timed his run perfectly to finish off Christian Benteke's cushioned header after quick thinking by Philippe Coutinho.
Firmino then sealed the points, beating Heurelho Gomes with a deflected strike, while Odion Ighalo had Watford's clearest chances, but the out-of-form forward saw his best effort saved superbly by Simon Mignolet.
Liverpool have now lost only one of their past 12 Premier League fixtures at Anfield and their top-six dreams are still alive due to their latest home win, while Watford remain 13th.
Ighalo almost opened the scoring with a spectacular strike after seven minutes, seizing on Allen's loose pass and sending a long-range lob just over the crossbar.
The young Liverpool side struggled for cohesion in the final third, but Coutinho provided a warning with a bending effort that just cleared the post.
And Jurgen Klopp's men took the lead after 34 minutes.
Watford were caught cold by a quickly taken free-kick as Benteke nodded Coutinho's cross into Allen's path and the Wales international beat Gomes to the ball, stabbing home with the game's first shot on target.
Coutinho should have doubled Liverpool's lead shortly after half-time, the playmaker miscuing his finish terribly after playing a one-two with Benteke.
Gomes then saved from Coutinho after more good link-up play with Benteke.
Liverpool were indebted to goalkeeper Mignolet, who made a wonderful fingertip save to deny Ighalo after 55 minutes, the 16-goal striker's goalless run stretching to 12 league games.
Almen Abdi whipped a free-kick over the crossbar after 67 minutes as Watford, who have scored just four goals in their last nine away Premier League matches, sought an equaliser.
Substitute Steven Berghuis then shot straight at Mignolet from an excellent position, but Liverpool's win was confirmed after 76 minutes.
Sheyi Ojo's pressing forced a mistake by Ikechi Anya, which led to Firmino advancing on goal, the Brazilian hitting a deflected shot that Gomes got a hand to and should have kept out, despite it taking a nick off Anya.
Benteke almost added the goal his industrious display deserved with eight minutes to go, but Gomes shovelled his shot around the post, before Jordon Ibe struck the outside of the woodwork late on as Liverpool cruised to victory.
