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The Chelsea loanee converted a 35th-minute penalty to give the Baggies, who handed a substitute appearance to Peter Odemwingie, an advantage at the break.
He then made sure of the points with a fortunate second which condemned Sunderland to a fourth defeat in six games.
Later in the first period, he chalked off a Lukaku strike and instead brought the play back for an earlier foul on James Morrison.
Lukaku was not to be denied a second time, though, as he beat Simon Mignolet from the spot after Craig Gardner was adjudged to have handled - another decision which angered the Black Cats.
Mignolet was to have a helping hand in his Belgian compatriot's second, blasting a clearance off the Baggies forward and into the net.
Sunderland strike pair Danny Graham and Steven Fletcher, starting a game together for the first time, were each guilty of missing several chances, but Stephane Sessegnon did pull one back for the visitors.
He bent a deflected shot past Foster into the bottom corner, but West Brom hung on to claim the points that see them climb above Liverpool into seventh place in the Premier League table.