Two first-half strikes from Robbie Keane secured an easy three points for the Reds, who go above Chelsea for 24 hours at least.
Still trying to justify his £20million price tag, the first chance fell to Keane after 13 minutes when a neat throughball from Javier Mascherano found the striker unmarked inside the box with his back to goal.
Unaware of the amount of space he had, Keane quickly spun and shot but the weak effort posed little threat to Scott Carson.
Liverpool started to pile the pressure on to the visitors and long-range efforts from Mascherano and Dirk Kuyt were getting closer to the mark.
Having been camped in the West Brom half, it was only a matter of time before the Reds made a breakthrough and it came in the 34th minute when a quick counter from the halfway line was neatly finished by Keane to open his Premier League account for his new club.
A strong interception from Jamie Carragher in the centre circle sent the ball straight to Gerrard, who was given time to pick his pass and after letting the ball roll across his path, Keane finished with his first touch over the sprawling keeper.
The home side went searching for another from the restart and eight minutes later a quick break from a West Brom corner released Keane to net his second of the match and fourth of the season.
A fumble from Pepe Reina saw the Liverpool keeper spill a routine catch inches wide of his own post but, having not beaten the first man with the corner, the Reds swiftly passed their way up field and a ball to Keane saw him skip around Carson and finish with his left into an open goal.
The second half started where the first left off with the home team throwing everything at a nervous looking West Brom defence and it took a few minutes before they carved open another chance.
With Gerrard pulling all the strings in the middle of the park it was him that released Albert Riera down the left who whipped over a deep cross searching for Kuyt, but good defending from Paul Robinson held the striker away from the ball at the back post.
On a hat-trick, Keane was proving to much for the Baggies back four and his persistence on the hour-mark found him out-muscling the towering figure of centre back Ryan Donk, but his touch took the ball to close to Carson who smothered the ball easily.
Despite having the match of his short Liverpool career, Keane was once again substituted before full time with Fernando Torres coming on following his injury lay-off.
Almost resigning themselves to defeat, West Brom had even more salt rubbed into the wounds after a lacklustre pass from Robinson led to the ball finding Alvaro Arbeloa, who dispatched an accurate shot into the top corner for his first goal of the season in the 90th minute.