Tony Pulis's side have inconvenienced other UEFA Champions League aspirants of late, beating Arsenal 3-1 and holding Manchester United to a 0-0 draw.
But they were unable to lay a glove on Liverpool for much of a listless encounter, and what is normally an area of strength for Albion proved to be their downfall.
Firmino was allowed too much room to net his 11th Premier League goal of the season as the hosts' set-piece defending failed them in first-half stoppage-time.
Jurgen Klopp's side provided few of the thrills normally associated with the division's top scorers, with Sadio Mane's void in attack one they will struggle to fill over the closing weeks, but Liverpool never looked like letting their control slip during the second period.
They return to third place, two points above Manchester City having played a game more.
West Brom midfielder Claudio Yacob carelessly coughed up possession inside his own half in the 15th minute, allowing Philippe Coutinho to scamper towards goal and play in Firmino, who dragged wide left footed.
Nacer Chadli should have added to his five goals for Albion but swung a boot at fresh air after Matt Phillips hooked the ball towards him at the back post.
Coutinho stretched to volley off target on the end of Firmino's raking 24th-minute pass but Liverpool were struggling for fluency – Adam Lallana's ongoing absence through a hamstring injury being keenly felt in midfield.
Phillips was the provider once more for the hosts when Hal Robson-Kanu found space between the Liverpool centre-backs but scuffed tamely at goalkeeper Simon Mignolet.
With a forgettable half meandering towards its conclusion, Klopp's men took the lead in stoppage-time.
Chris Brunt pulled back Divock Origi, earning a booking for his troubles, and the Northern Ireland international's indiscipline was punished when Lucas Leiva flicked on James Milner's delivery from the right and Firmino headed home.
Liverpool almost added a wonderful second 11 minutes into the second period.
Georginio Wijnaldum slid a nicely-weighted pass into Firmino's path and the goalscorer chipped across the West Brom box, where Milner charged forward from left-back to volley over.
West Brom's dour form in front of goal meant Liverpool were scarcely tested until 10 minutes from time.
Phillips collected a return pass from Salomon Rondon after the substitute powered towards the opposition penalty area, but Mignolet stood firm to block his effort behind.
Pulis's men would go no closer to getting on terms – the Arsenal win before last month's international break standing as the only game in the last seven where they have found the net.
Goalkeeper Ben Foster ventured up for a stoppage-time corner to try and improve this record but found himself stranded on the right wing. Liverpool substitute Alberto Moreno eyed up West Brom's unguarded goal but, like all other attempts during the second half, his shot was off target.
Key Opta stats:
- Liverpool have won 66 points from 33 games this season; six points more than they picked up in the entirety of 2015-2016.
- West Brom have failed to score in four consecutive Premier League games for the first time since April 2003.
- Roberto Firmino has now surpassed his Premier League goal tally from last season (10 in 2015-2016, 11 in 2016-2017).
- Since the start of last season, Firmino has been directly involved in 34 Premier League goals (21 goals, 13 assists), more than any other Liverpool player.