A superb strike from Zoltan Gera, Peter Odemwingie's penalty plus a header from on-loan newcomer Romelu Lukaku made it a miserable day for new Reds boss Brendan Rodgers.
Liverpool also had defender Daniel Agger sent off early in the second period and looked a shambles at the back in the final half hour.
Their day was summed up by striker Luis Suarez, who could have had a hat-trick before Liverpool were swept aside after Agger's dismissal.
Albion, who also saw Shane Long miss a spot-kick, got to grips with the midfield area with James Morrison an inspirational figure.
But for Rodgers this was a reminder that there is much work to do before Liverpool re-emerge as a potent force.
Albion started brightly and Liam Ridgewell was only just too high with a 20-yard drive while Long's chip flew over the bar after he dispossessed Lucas Leiva.
But the first save of note came from Baggies keeper Ben Foster who parried away a powerful 20-yard drive from Suarez after a weaving run.
The home side were fortunate to win a free-kick when Long stumbled over Martin Skrtel, but Steven Reid was unable to take advantage as his set piece was deflected wide.
Suarez looked sharp and turned inside Gareth McAuley before forcing another save out of Foster.
He should have scored after half an hour when heading over from the edge of the six yard box after attacking a Glen Johnson centre.
Albion came back strongly in the final minutes of the half which culminated in them taking the lead after 42 minutes.
Glen Johnson was booked for a foul on Peter Odemwingie and, although Reid's free-kick was deflected wide, the resulting corner led to the deadlock being broken.
Morrison's centre was headed away by Skrtel but Gera seized on the ball and in an instant flashed an unstoppable rising shot past Pepe Reina from 20 yards out.
Suarez's frustration boiled over in first half injury-time when he was yellow carded for dissent.
Liverpool started the second half on the offensive and Suarez floated a free-kick wide after being brought down on the edge of the box by Youssouf Mulumbu.
But the Baggies weathered the initial storm and doubled their lead from the second of two penalties awarded them in the space of six minutes.
The Reds were reduced to 10 men after 58 minutes when Agger pulled back Long just inside the box only for the Republic of Ireland striker's weak spot kick to be saved by Pepe Reina.
But referee Phil Dowd awarded another penalty when he adjudged that Skrtel had tripped Long although this seemed a harsh decision.
This time Odemwingie took the spot-kick and hammered the ball past past Reina.
Suarez missed a golden chance to reduce the arrears when he shot over from six yards after Foster had dropped a Steven Gerrard corner.
But Albion were now carving chances at will and Morrison shot wide with the goal at his mercy before substitute Lukaku put the icing on the cake for Albion after 77 minutes.
Mulumbu's shot was deflected into the path of Ridgewell and his lovely lob to the back post was headed in at the far post by the on-loan Chelsea player.
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