Goals from Sadio Mané and Philippe Coutinho were enough to take all three points, despite scare after Gareth McAuley to reduced the deficit late on.
The Reds now sit in second spot, level on points with Arsenal.
Jürgen Klopp made just the one change from the goalless draw with Manchester United on Monday night. Adam Lallana returned to the starting XI, with Daniel Sturridge dropping to the bench. Roberto Firmino led the line for the hosts.
The visitors also made a single change from theur line-up, as defender Jonas Olsson made his first start since August, replacing the suspended Jonny Evans.
Mane opens scoring for hosts
With all expectations of Tony Pulis' side rolling up to Merseyside to defend with 10 men behind the ball, West Brom were looking to utilise both flanks with the occasional foray forward. The plan worked until the 20th minute.
After the ball was won on the half-way line Emre Can raced raced toward the Baggies' goal. The German slipped a ball wide to the overlapping Roberto Firmino, who floated a curling cross into the penalty area, as Sadio Mané slotted a low volley past Ben Foster to open the scoring.
As West Brom looked to regroup, both Lallana and Philippe Coutinho continued to pull the strings for The Reds. Indeed it was the Brazilian who doubled their advantage.
After a poor clearance, the ball fell to the feet of Mané. The Senegalese drifted wide and layed the ball off the Coutinho, who dodged the advances of both Craig Dawson and Gareth McAuley, turned and rifled a shot into the bottom corner of the Liverpool net. At the break, Klopp's men were in control at 2-0.
Hosts look to assert dominance
In a half with relatively few chances, the hosts were keen to keep a hold on proceedings. Indeed only a superb block from Jonas Olsson six yards-out prevented a third goal after 65 minutes.
West Brom rarely threatened their opponents goal, as Salomon Rondon remained an isolated figure up front. It seemed that unsurprisingly, a set-piece was the most likely opportunity to garner a foot-hold in the game.
McAuley reduces deficits for West Brom
Indeed it was the case once more. The Baggies forced a corner and after from the delivery, a bobbling ball ricocheted onto McAuley's shoulder. The Northern-Irishman composed himself to half-volley past Loris Karius and into the Liverpool net.
Seemingly coasting to victory, Klopp's side were suddenly wobbling as the game opened up in the final ten minutes. Foster denied Firmino twice, once from a header and from close range as the Baggies' stopper kept West Brom in the game.
As the visitors pushed for a leveller, Liverpool almost sealed the three points in stoppage time from substitute Georginio Wijnaldum's long-range effort, but Jürgen Klopp's men held on to win for the three points, to sit second in the league table.