Carroll scored in the 45th minute to hand the visitors an easy win after Charlie Adam had put the Merseysiders ahead following a controversial penalty award by referee Lee Mason.
Roy Hodgson’s men offered very little in resistance to the Reds’ dominance and The Baggies failed to really test Pepe Reina in the away goal.
The tone of the match was set within three minutes when Liverpool earned an early corner. Adam took the set-piece, finding target-man Carroll, but the striker’s effort lacked both pace and direction.
However, Liverpool were rewarded for a strong start when Jerome Thomas was penalised for a foul on Luis SuÃ¡rez in the box.
Mason had originally waved play-on before his linesman frantically signalled that an infringement had occurred and he pointed to the spot.
Adam, who had to wait several minutes while Mason dealt with the vociferous complaints from the home side, calmly placed his penalty into the left corner.
And the visitors could have had a second spot-kick just 10 minutes later.
SuÃ¡rez embarked on a mesmerising run down the right wing, finding Carroll in the Baggies’ area – but the striker’s headed effort was blocked by the hand of Steven Reid.
Mason, perhaps conscious of his controversial award minutes earlier, pointed for a corner kick.
The home side offered little in the first half as Somen Tchoyi was kept quiet by Daniel Agger and Martin Skrtel – the Liverpool defence coping well without the commanding presence of injured centre-half Jamie Carragher.
After 36 minutes, SuÃ¡rez was handed a glorious opportunity to score his fifth goal of the season, but the Uruguay forward ballooned his effort over the crossbar from six-yards.
Fortunately for Liverpool’s No7, the miss was rendered meaningless on the stroke of half-time as Carroll all but secured the Reds’ third away win of the season.
A quick counter-attack saw Lucas find SuÃ¡rez, who delicately pushed the ball into Carroll’s path for the striker to slot past Ben Foster.
Hodgson’s team-talk at the interval appeared to have little impact on his side’s performance and within seconds of the restart Jordan Henderson had a chance to test Foster – but the midfielder misfired a tame effort wide.
The Baggies struggled without the movement and tireless running of Shane Long and their only real sight on Reina’s goal came when Tchoyi managed to wrestle free of Agger and unleash a low drive across the the six-yard box which the Liverpool captain watched past his post.
Kenny Dalglish’s team could have extended their lead in the final quarter of an hour.
SuÃ¡rez surged forward, squaring to Carroll – and the England international chose to ignore the screams of Henderson who was free to his right, and screwed his shot well wide.
In stoppage time, Liverpool substitute Craig Bellamy burst into the area and teed up Stewart Downing – the winger smashed his shot into the base of Foster’s post and the rebound favoured the home side.
The victory pushes Liverpool back into fifth place ahead of Arsenal and Tottenham, while West Brom remain in 13th place.
West Brom: Ben Foster, Jonas Olsson, Billy Jones, Gareth McAuley, Steven Reid, Chris Brunt, Jerome Thomas, Somen Tchoyi (Simon Cox, 71), Youssuf Mulumbu (Graham Dorrans, 63), Paul Scharner (James Morrison, 58), Peter Odemwingie.
Liverpool: JosÃ© Reina, JosÃ© Enrique, Glen Johnson, Daniel Agger, Martin Skrtel, Stewart Downing, Lucas Leiva, Charlie Adam, Jordan Henderson, Andy Carroll, Luis SuÃ¡rez (Craig Bellamy, 82).
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news