The Brazilian headed in the only goal of the game just before half-time to settle affairs at the Hawthorns and extend his side’s unbeaten run to seven matches.
West Brom will rue golden opportunities missed by Nacer Chadli and Matt Phillips, while James Milner should have volleyed in a second for Liverpool early in the second half and Alberto Moreno missed an open goal from 35 yards late on.
The victory moves Jurgen Klopp’s side up to third on 66 points – nine clear of fifth-placed Everton – with five games to play. West Brom remain in eighth position.
Brazilian duo Firmino and Philippe Coutinho were restored to the starting line-up after both scored from the bench against Stoke last week and they combined to create Liverpool’s first chance, Firmino slotting narrowly wide across Ben Foster from his team-mate’s pass.
Phillips was the chief architect for West Brom in the first half with his scuffed shot almost being turned in by Hal Robson-Kanu in the third minute and he later crossed for Chadi, who somehow failed to connect from six yards with the goal gaping.
Firmino guided a volley wide from a Coutinho cross and Robson-Kanu shot straight at Simon Mignolet as the first half looked destined to end goalless – until Chris Brunt fouled Divock Origi in added time.
From Milner’s free-kick, Lucas headed the ball on for Firmino, who evaded the attention of Craig Dawson to nod past Foster from six yards and give Liverpool the lead.
The goalscorer almost created a second in the 57th minute when he sent a pin-point cross in the direction of Milner at the far post – however the unmarked left-back volleyed over the bar from inside the six-yard box.
Firmino was then flagged offside when he headed Lucas’ ball across goal and Origi turned it into the net, while Coutinho blasted an effort over the bar just after the hour mark.
Tony Pulis sent on three substitutes – James Morrison, James McClean and Salomon Rondon – with more than 25 minutes left to play and the latter carved out a glorious opportunity with 10 minutes left.
Rondon played a perfect pass through to Phillips who raced beyond the defence and only had Mignolet to beat, but the Liverpool goalkeeper rushed out to make a crucial save.
Substitute Moreno should have scored a second in injury-time when goalkeeper Foster went forward for a West Brom corner and Liverpool broke away – but he haplessly failed to steer his 35-yard effort on the empty goal on target.
Foster was effectively playing in midfield in a chaotic final minute, but Liverpool held on to take all three points and will continue their top-four push at home to Crystal Palace live on next week’s Super Sunday.
West Brom will have 13 days to reflect on their disappointment before they welcome Leicester to the Hawthorns on April 29.