The Baggies took the lead late in the first half when Zoltan Gera drilled a shot past Pepe Reina after Reds striker Luis Suarez had missed two great chances to give Liverpool the advantage.
Liverpool defender Daniel Agger was shown a red card after he brought down Shane Long in the area after the break but the striker was unable to convert from the spot, his weak effort easily saved by Reina.
However, Long quickly atoned when he was tripped by Martin Skrtel to claim another penalty, with Peter Odemwingie firing into the bottom left corner, before substitute Romelu Lukaku sealed the win in the 78th minute with a close-range header.
Swansea midfielder Michu scored a goal in each half on his Premier League debut as the Swans thumped QPR 5-0 at Loftus Road.
The Spaniard scored this season's first goal in the Premier League when his shot crept past goalkeeper Robert Green in the eighth minute before he doubled his tally after the break thanks to Wayne Routledge's inch-perfect ball from the left which he fired into the net.
Nathan Dyer fired the third, again from a Routledge assist, before he beat the offside trap to score Swansea's fourth, with Scott Sinclair's strike rounding off new manager Michael Laudrup's perfect start to the season.
Fulham thumped Norwich 5-0 at Craven Cottage thanks to a dominant performance and a brace by Mladen Petric.
Republic of Ireland international Damien Duff opened the scoring when he latched on to the end of John Arne Riise's diagonal long ball from the left in the 25th minute before Petric headed the home side's second with five minutes remaining in the first half.
The striker then added his second before Alex Kacaniklic's goal and Steve Sidwell's 87th-minute penalty wrapped up the win.
Stoke drew with Premier League new boys Reading 1-1 at the Madejski Stadium after they gave away a penalty and were reduced to 10 men in the dying minutes.
Michael Kightly fired Tony Pulis' side into the lead from close range, with the ball slipping through goalkeeper Adam Federici's fingertips, but the Royals salvaged a point when Adam Le Fondre equalised from the spot as Dean Whitehead was sent off for his second bookable offence.
Elsewhere, Kevin Nolan's strike gave West Ham a 1-0 win over Aston Villa in their opening game at Upton Park.
Nolan scored from close range in the 40th minute from Ricardo Vaz Te's assist to edge the Premier League new boys ahead before they had a penalty shout turned down after the break.
Arsenal dominated Sunderland at Emirates Stadium but were unable to find the breakthrough as they drew 0-0.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.