Zoltan Gera put the hosts ahead with a wonderful long-range chest and volley late in the first half, before Peter Odemwingie added a second from the spot after Martin Skrtel fouled Shane Long just before the hour mark.
Long had only just missed a penalty himself, taken after Dan Agger brought him down, the Denmark defender sent off for denying a clear run at goal.
Playing the final half hour a man light took its toll as loanee Romelu Lukaku headed a third on his debut, with the Baggies denied a fourth by good goalkeeping from Pepe Reina.
Despite acquiring a highly-rated young manager and several new signings, Liverpool showed no improvement from last season: Luis Suarez was as skilful - and wasteful - as ever, spurning a handful of good chances after wowing the crowd with his dribbling ability.
Meanwhile his team-mates constantly gave the ball away, Steven Gerrard responsible for the incident which saw Agger dismissed and the likes of Fabio Borini, Lucas and Stewart Downing constantly failing to find their destinations.
The Baggies, meanwhile, had a new manager of their own as former Reds assistant Clarke finally started his career as a number one. The hosts were tidy in possession, direct on the counter attack and solid in defence, but they were helped by a shaky Liverpool defence that constantly got its wires crossed.
The first half was even and entertaining, with Liverpool seeing plenty of the ball but making few telling passes, West Brom more accurate as both sides created some decent opportunities.
The first went to Liam Ridgewell, who toe-poked over after a fine passing move involving Claudio Yacob, a free-transfer debutant who controlled the midfield and effectively snuffed out Gerrard.
Liverpool did have their moments but, as per last season, were wasteful, Suarez particularly guilty as he headed over from point-blank range after a fine Glen Johnson cross, before firing one effort straight at Ben Foster and another well wide as he continued to show great dribbling but poor composure in front of goal.
The Uruguayan did unleash one rasping drive that was well-saved by Foster, but his frustration was all-too evident as he picked up a booking for dissent late in the half.
That came after the Baggies had opened the scoring, and it was some goal too as, after Liverpool cleared a corner, Gera took the ball on his chest before firing a wonderful volley into the top corner.
Gera’s shared delight with his fans came with context: the Hungarian returned to West Brom from Fulham last summer, but missed the majority of the season through injury.
Rodgers needed to liven things up in the second half. While they started directly and promisingly, the bad habits of last season – poor final balls from Downing, Gerrard going missing, Suarez unable to match his ability with any kind of finish – all resurfaced.
There were two new signings but neither had their best game. Joe Allen was the most composed of Liverpool’s midfielders but had little overall impact, while Fabio Borini had a poor Premier League debut, missing one good chance, taking a few dives but otherwise AWOL.
Liverpool were committing bodies forward but that just played into West Brom’s hands. The over-commitment was punished when, just before the hour mark, Gerrard gave the ball away: Long raced clear, was fouled by Agger, winning a penalty as the Dane was shown a straight red card for denying a goalscoring opportunity.
When Long finally stepped up to take the spot-kick – Liverpool had replaced Downing with Jamie Carragher in the interim – he practically passed the ball into Reina’s arms, one of the worst penalties you will see.
Self-destruction does not come lightly to Liverpool but, when it does, it is usually spectacular. With Agger gone, it was Martin Skrtel’s turn as the Slovakia defender dithered on the ball in his own box, allowing Long to nick it away from him before tripping the Ireland forward for a second penalty in almost as many minutes.
Long stepped aside for this one and it was a good decision as Odemwingie smashed a ferocious low spot-kick past Reina.
James Morrison then missed a Suarez-style sitter after unselfish play by Marc-Antoine Fortune, but Liverpool continued to commit - while the bravery of introducing Joe Cole was commendable, that too ended in farce as he re-injured his hamstring minutes after coming on.
That was the signal for Liverpool to turn full-circle back to last season as Andy Carroll was thrown on, the long balls subsequently chucked high into the Baggies box. In the meantime, West Brom had added a third as on-loan Chelsea striker Lukaku rose unmarked to head home his first Premier League goal, courtesy of a lofted cross by Ridgewell.
Lukaku had a few more half chances to add to his tally, as did Youssuf Mulumbu and Fortune, who forced an excellent stop by Reina.
The away fans were leaving in droves but they missed little as both sides willed on the final whistle, West Brom having done more than enough and Liverpool just desperate to go home.