The striker scored both of the Baggies' goals as he converted a penalty to open proceedings, before grabbing a slightly more fortuitous second as, after chasing down a backpass, Simon Mignolet's clearance rebounded off him and into the empty net.
Although a Stephane Sessegnon strike 10 minutes from time resulted in a frantic finish, the home side bagged the three points, leaving them seventh and only eight points adrift of the top four.
Lukaku's double also cements him as West Brom's top goalscorer, the 19-year-old having now netted 12 goals in 25 games, and former defender Clarke was clearly elated with his on-loan striker as he admitted he himself would not fancy playing against him.
"He's [Lukaku] in a great run of form and has done really well for us, he had a partner up front with him today which helped him," he told reporters.
"It gave him space to make the runs in behind defenders that he likes to make. As a former defender I certainly wouldn't like to face up to him."
Martin O'Neill, meanwhile, was more concerned with the referee's performance as, although he accepted the penalty decision against his side for the first goal, he felt his side should have had a spot-kick themselves after Adam Johnson's cross struck Gareth McAuley on the arm.
"My opinion is that they were both penalty kicks," he told reporters. "With West Brom's, even though the ball has hit Craig Gardner close in, we were told at the start of the season that with that sort of incident that if you were putting your hand in the air then that is a penalty.
"At the same time, it was a penalty at the other end. It was the same situation and therefore the referee should have given it."