The visiting Baggies dominated large parts of the match and forced Wolves goalkeeper Wayne Hennessey into action with just one minute on the clock. Hesitancy in the Wolves defence presented Jerome Thomas with a goalscoring opportunity but his effort was saved by the Welsh keeper.
Hennessey was again called into action to deny Odemwingie and Paul Scharner in quick succession.
However, Hennessey was unable to prevent West Brom from taking a 1-0 lead in the 34th minute. Odemwingie cut inside his marker before shooting past Hennessey via a deflection off Wolves midfielder David Edwards.
Despite struggling to capture any sustained possession, Wolves managed to draw themselves level in first-half stoppage time. Sylvan Ebanks-Blake and Steven Fletcher linked for the latter to swivel on the edge of the area and send his left-footed effort beyond the reach of Ben Foster.
West Brom's Marc Antoine Fortune had the first chance of the second half, but Hennessey was on hand to tip his powerful effort wide of goal. However, from the resultant corner, West Brom went in front again. Gareth McAuley struck the post with a header and when Wolves failed to clear the rebound, Jonas Olsson volleyed past Hennessey in the 64th minute.
Wolves' response was positive and they went close to equalising in the 71st minute when Roger Johnson's headed effort struck the bar, while up the other end Odemwingie had a shot cleared off the line by Kevin Foley.
West Brom's decisive third goal arrived in the 77th minute. Liam Ridgewell and Olsson exchanged passes for Odemwingie to turn the ball into the net from close range.
Keith Andrews came off the bench to add fourth for the Baggies, before Odemwingie wrapped up his hat-trick when he finished off a counter-attack move in the 88th minute.
Wolves manager Mick McCarthy and his side left the pitch to a series of jeers from the home support.