After a drab first half, the match burst into life after the break as Youssouf Mulumbu fired the Baggies in front within two minutes of the restart.
However Jean Beausejour provided an immediate response turning in his first Premier League goal a minute later.
But James Morrison restored the advantage with a classy finish on 58 minutes and Paul Scharner wrapped up a vital victory with a header from a tight angle 18 minutes from time as Albion leapfrogged the Carling Cup winners.
