Odemwingie followed up his hat-trick against Wolves with another impressive performance, with James Morrison and Keith Andrews also on target.
Roy Hodgson's side, who had collected only one point from their previous six home games, dominated against the previously on-song Black Cats.
Odemwingie looks full of confidence, in contrast to the injury-hit player who has struggled for much of the campaign, despite playing in a wide role.
Central striker Marc-Antoine Fortune was also a key player with his hold-up play while Morrison had another effective game in midfield.
But Albion controlled all departments and snapped away at the challenges in midfield, not allowing Martin O'Neill's side to settle.
O'Neill, who is 60 on Thursday, will hope this is a one-off performance after transforming Sunderland's fortunes and only Craig Gardner posed any sort of goal threat.
Odemwingie needed only three minutes to break the deadlock. Youssouf Mulumbu supplied a teasing cross from the left of the Sunderland box and Odemwingie got in front of Kieran Richardson to send his glancing header past Simon Mignolet.
It was the Nigerian international's ninth goal of the campaign.
Albion dominated possession and midfielder Andrews tested Mignolet with a dipping drive.
It was 26 minutes before the visitors had their first shot on goal and then Gardner dragged his low drive well wide.
Albion continued to play with purpose and Mignolet turned aside a Jonas Olsson header from a Steven Reid free-kick. Then Mignolet parried a curling Morrison attempt after a period of neat one-touch football.
But Albion's perseverance paid off with Morrison doubling their lead after 41 minutes.
The Scotland international was perfectly placed to head home a fine cross from Jerome Thomas from close range with the Sunderland defence at sixes and sevens.
O'Neill made a double half-time switch with new England recruit Fraizer Campbell and fellow striker Nicklas Bendtner, who was playing with a face mask, replacing Kieran Richardson and Jack Colback.
The Black Cats were now playing three up front and Albion keeper Ben Foster clung onto a low drive from Gardner.
But their bold policy left them prone to being caught on the counter-attack and after 49 minutes Odemwingie put Albion 3-0 ahead.
Foster's quick throw out to Morrison left Albion in a two versus two attacking position and they took full advantage. Morrison picked out the run of Fortune who squared the ball across the box to Odemwingie who made no mistake with a low drive.
Thomas came close to making it 4-0 when he cut inside and saw his curling attempt hit the crossbar.
Gardner was the only player posing a threat for Sunderland and a swerving shot hit the body of Foster. Albion continued to look more menacing and Michael Turner cleared a goal-bound shot from Fortune.
Reid then produced a superb block tackle to halt Stephane Sessegnon as he prepared to shoot inside the West Brom box.
John O'Shea became the first player to be yellow carded for a challenge on Morrison. Graham Dorrans was also booked a minute later for a mis-timed tackle on Phil Bardsley
Andrews made it 4-0 in injury-time with a curling shot after good play between Morrison and Dorrans teed up the chance.