Hot on the heels of their impressive win at Stoke last weekend, which was their first in the Premier League on the road this year, Liverpool clinched another precious three points away from Anfield and once again Roberto Firmino made the telling contribution.
Was involved in the few things that Liverpool did well.
They return to third place, two points above Manchester City having played a game more.
The visitors could have extended their lead after halftime but James Milner blazed a glorious opportunity over the bar and Divock Origi had a goal ruled out for offside.
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.
Despite their struggles, the Baggies began brightly and Hal Robson-Kanu directed Matt Phillips' effort wide but Liverpool gradually took control and almost went ahead after 15 minutes.
Firmino won it seconds before half-time, heading in James Milner's free kick after Lucas had flicked it on.
And as West Brom pushed for an equaliser, and with their goalkeeper joining in the set-pieces, the reds twice found themselves faced with an empty net.
Firmino, of all people, lost the ball to Salomon Rondon and he teed-up Phillips only for the winger to be thwarted by the on-rushing Mignolet.
West Brom: Ben Foster 5, Craig Dawson 6, Gareth McAuley 6, Jonny Evans 6, Chris Brunt 5, Darren Fletcher 6, Claudio Yacob 6, Nacer Chadli 5, Jake Livermore 5, Matt Phillips 5, Hal Robson-Kanu 5. Substitute Alberto Moreno ran upfield on the break and with Foster stranded and the goal open, he curled a 40-meter shot wide of the post.
- 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.