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Referee Roger East was in the spotlight throughout the opening 45 minutes, denying each side what they deemed to be legitimate goals.
The home side were left equally frustrated when Lukaku's strike was chalked off, with East pulling the play back for a foul on James Morrison.
He was in the thick of the action again moments later, awarding West Brom a penalty for an apparent handball by Craig Gardner.
Lukaku stepped up to convert the 35th-minute spot kick for his 11th of the season.
Fletcher struck the post with a low drive and then miscued a rebound over the crossbar after Foster had parried Graham's preceding effort.