A Charlie Adam penalty and Carroll's third goal of the campaign confirmed Liverpool's superiority in the game, but it was the way that Carroll and Luis Suarez gelled which would have given the most satisfaction to Reds boss Kenny Dalglish.
With Adam and Lucas Leiva running the show in the centre of the park and Daniel Agger impressive in defence, Liverpool had few problems in chalking up a third away league win of the campaign.
It ended the Baggies' run of 11 points from the last six games, but more accomplished sides will find it hard to deal with Carroll and Suarez in this form.
Liverpool, without the injured Steven Gerrard (ankle) and Jamie Carragher (calf), were the first to settle and Suarez seized on a long ball from Jose Enrique only to be let down by his control.
However, Adam put Liverpool ahead from the penalty spot after only eight minutes. Suarez was bundled into by Jerome Thomas and referee Lee Mason pointed to the spot after his assistant Gary Beswick flagged for a foul.
Albion's players were incensed by the decision but up stepped Adam to send Ben Foster the wrong way from the spot for his second goal of the campaign.
Liverpool had appeals for a second penalty rejected when Carroll's header from Suarez's cross struck the hand of Steven Reid.
Jonas Olsson became the first player to be yellow carded after 35 minutes for a reckless challenge on Carroll.
Suarez had a chance to increase Liverpool's lead after 35 minutes when Martin Skrtel squared a deep Adam corner back across the box. But the Uruguayan shot wide from eight yards out.
Then after 45 minutes Carroll made it 2-0. Lucas' fine pass picked out Suarez and he released Carroll who clipped wide of the advancing Foster for his fifth goal in 21 games for Liverpool.
Liverpool began the second half on the offensive and Henderson failed to make proper contact on his shot after Carroll found him in space.
Albion came close for the first time after 47 minutes when Somen Tchoyi was inches wide with his low cross shot.
But Liverpool were quickly back in command and Carroll should have done better when an Adam shot ballooned up into his path.
Suarez was proving hard to contain and he shot over from a narrow angle.
A long raking pass from Adam released Suarez who cut inside the box but he was eventually crowded out and Foster collected.
Albion were forced into a change with Scharner picking up a knee injury and replaced by James Morrison.
Jose Enrique galloped forward to force Foster to finger-tip his shot over the bar and then the keeper blocked a Carroll volley after more good play by Suarez.
Carroll found himself in acres of space on the edge of the box but shot wide when Jordan Henderson was unmarked.
With nine minutes left, Dalglish made his first substitution with Suarez making way for Craig Bellamy - his 250th Premier League appearance.
Olsson headed wide from a Chris Brunt corner but it was too little, too late from the Baggies and in injury time the woodwork denied Downing his first Liverpool goal.