Nigerian forward seals West Brom's first EPL win in 15 months.
Albion had not scored in their last four Premier League games, stretching back to a 3-1 home victory over Wigan in May 2009.
West Brom manager Roberto Di Matteo, looking to start fresh after last week's dismantling by Chelsea, made a handful of changes to his side.
Odemwingie was given the start, as Roman Bednar dropped to the bench while Jonas Olsson was recalled to the Baggies' starting line-up in place of Pablo Ibanez.
With Sunderland captain Lee Cattermole suspended, manager Steve Bruce gave a first start to Cristian Riveros and Paulo Da Silva came in for the injured John Mensah in the Black Cats' only other change.
Odemwingie had the best chance for the home side early on, as he dragged a shot wide of the far post, which would have been a dream start as his transfer from Lokomotiv Moscow had only been confirmed 24 hours earlier.
International clearance arrived in time for him to play, and the 29-year-old was right in the thick of things, latching on to Chris Brunt's measured through-ball in the eighth minute and shooting narrowly wide.
West Brom continued to press forward with James Morrison sending a volley wide.
Sunderland's Darren Bent, wearing the captain's armband in Cattermole's absence, looked to have beaten the offside trap, only for the referee's assistant to raise his flag as the England striker fired at Scott Carson.
Sunderland then won a free-kick just outside the box, but former Baggies man Kieran Richardson could only curl it over the bar.
Moments later the visitors had another chance, but Bent struck a free-kick straight into the West Brom wall.
Albion responded with Morrison breaking down the right, beating two men and delivering a cross that was just too high for Brunt.
Bent put a header wide just after half-time, as a perfect cross was put past the near post.
Albion won a free-kick in a decent position, only for Graham Dorrans to put it high over the bar.
Giles Barnes was brought on at half-time for Jerome Thomas and produced a useful cross, but Mignolet was able to dive on it.
Richardson was next to try his luck from a set-piece in the danger zone and, although going closer than Dorrans, he also missed.
Brunt then rose to head Barnes' cross goalwards, but Mignolet made a comfortable catch.
With a little over 20 minutes remaining, Bruce put on Danny Welbeck and Boudewijn Zenden as the visitors went in search of a winner, but it was Odemwingie who would be the hero, as Gonzalo Jara fed a pass through the Sunderland defense to put the Nigerian clean through to toe-poke home in the 81st minute.
The Black Cats never looked like challenging again, and West Brom had their much-deserved win.
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