A Craig Gardner handball and poor Titus Bramble clearance were responsible for the Belgian's two goals, and Sunderland could not find an undeserved equaliser after a deflected Stephane Sessegnon gave the away side hope.
The headline team news came on the West Brom bench, with the selection of Peter Odemwingie in the matchday squad causing something of a stir with the home crowd following the Nigerian's much-publicised deadline day escapades. For Sunderland, January signing Danny Graham was selected alongside Steven Fletcher for the first time in an attacking-looking line-up.
The game started quietly as both sides looked to settle on the ball without threatening to open the scoring. In fact, the first half-chance of the game did not arrive until the 20-minute mark when Lukaku drifted a header wide from ten yards out.
It was a moment that kick-started the half into gear, and moments later Sunderland had three chances in succession to score. First Fletcher side-footed the ball against the left-hand post, and from the rebound Graham forced Ben Foster into a smart save. The ball then fell back to Fletcher, who fired over from the edge of the box.
Five minutes later Youssouf Mulumbu should have given the home side the lead, inexplicably missing from four yards out with a header when it looked easier to score, and two minutes later referee Roger East was involved in controversy when he failed to give West Brom the advantage when James Morrison had been fouled, and Lukaku tucked the ball passed Simon Mignolet.
However, three minutes later the Baggies were ahead. Chris Brunt crossed from the left and the ball hit Gardner on the hand, allowing Lukaku to nonchalantly finish from the penalty spot.
The goal gave the home side confidence, and they ended the half impressively as they looked to make the most of their dominance as the half-time whistle came as a relief to Sunderland, although the visitors did have their own penalty appeal for handball turned down.
West Brom continued to be dominant during the second half, and it became something of the Lukaku show. He scored his second on 70 minutes when a short backpass from Bramble allowed the forward to bear down on goal. Mignolet came rushing out, but his clearance rebounded off Lukaku and into the net.
The Belgian was comfortably the best player on show, and the contrast between the standing ovation Lukaku received when he came off for Odemwingie, who was roundly booed, was marked.
Two minutes later and Sunderland were back in the game, when Sessegnon curled home a shot from the edge of the area, beating Foster via an Olsson deflection.
Despite late chances, notably for James McLean who fired over in added time, West Brom were able to hold on for a home victory that took them to seventh in the Premier League.