Liverpool notched up a 10th successive league win to end 2005 on a high note.
West Brom came with a strategy to stifle Liverpool - a plan that worked for 52 minutes thanks to a succession of saves from keeper Tomasz Kuszczak.
Three of those saves were to deny Harry Kewell, but the Australian got his revenge when he sent in a cross that Peter Crouch headed past Kuszczak.
Crouch almost claimed a second with another header but this time Kuszczak cleared the ball with his feet.
Having fallen behind, West Brom attempted to come out of their defensive shell but they never really tested Liverpool goalkeeper Jose Reina.
As so often this season the foundations of this Liverpool win were built on captain Steven Gerrard's drive and Xabi Alonso's immaculate passing.
But on the left wing Kewell impressed as well and, had it not been for Kuszczak, the Australian might have had a hat-trick.
Two of those saves came in the opening quarter of an hour as the Polish keeper first beat away Kewell's effort from outside the box after Paul Robinson had casually given the ball away.
Kewell's next effort was even more ferocious, but the Australian's close-range shot was superbly tipped away by Kuszczak.
At times Kuszczak's goal seemed to be leading a charmed life, notably when John Arne Riise's shot emerged through a posse of players to come back off the post.
The ball fell to Kewell, but Kuszczak was quickly back on his feet to palm away the winger's shot.
Veteran defender Steve Watson played his part in frustrating Liverpool, coming to his goalkeeper's rescue three times with well-timed blocks.
It was not long before Kuszczak was back in action, the Pole beating away a Gerrard shot after the England midfielder swapped passes with Cisse.
Having held out for the first 45 minutes, West Brom fell behind seven minutes after the restart.
Kewell flighted in an inviting cross from the left for Crouch, who cleverly guided a header into the right-hand corner of Kuszczak's goal.
Kuszczak continued to defy Rafael Benitez's side as Liverpool searched for a second goal and just past the hour he got down to quickly to tip away a vicious Riise free-kick.
The Pole's best save of the game came with his feet rather than his hands when he brilliantly cleared a Crouch header, flicking out a leg just as the ball looked to have gone past him.
In stoppage time Gerrard went on one of his surging runs only to flash his shot narrowly wide.
The win kept Liverpool in touch with Manchester United, but the defeat for West Brom saw them to slip to fourth from bottom in the table.
Liverpool manager Rafael Benitez:
"The West Brom goalkeeper was the game's man of the match.
"He did a very good job. We tried everything - shooting, crossing and heading, but it was almost impossible.
"We controlled the game, but they made it very difficult for us as they played deep and with many players in front of the ball."
West Brom manager Bryan Robson:
"I'm pleased with the way we stuck at - I thought at one stage it was going to be our day.
"Tomasz Kuszczak has put on a great performance. Chris Kirkland has come back from injury but Tomasz has done nothing wrong.
"I wanted to make Liverpool a little bit edgy, but they deserved the win."
Liverpool: Reina, Finnan, Hyypia, Carragher, Riise, Luis Garcia, Gerrard, Alonso, Kewell (Sinama Pongolle 67), Cisse (Traore 89), Crouch (Sissoko 81).
Subs Not Used: Carson, Hamann
Goals: Crouch 52.
West Brom: Kuszczak, Watson, Curtis Davies, Clement, Robinson, Chaplow (Greening 65), Wallwork (Kamara 76), Albrechtsen, Carter, Campbell (Ellington 80), Horsfield.
Subs Not Used: Hoult, Moore.
Ref: A Wiley (Staffordshire).