The Swiss defended strongly throughout the match, but Lukaku converted two chances of three to give top-ranked Belgium the victory.
The result left Belgium with six points from two games in Group 2 of the top-tier League A, three points more than Switzerland. Iceland lost its two matches. Already Belgium's all-time goal scorer, Lukaku reached 45 goals in 78 international appearances.
After a smooth move started by Eden Hazard in the 58th minute, the ball ended up with the Manchester United striker and he hit home from about 12 meters (yards). Switzerland proved resilient after conceding the goal. In the 76th, Xherdan Shaqiri curled a free kick into the box and substitute Mario Gavranovic easily slotted home from close range after the Belgian defence failed to clear.
It came down to Lukaku to break the deadlock with six minutes left. He kept a cool head in the box and finished low through the centre for the decider.
"It was tough," Hazard said. "Two great goals."
(Reporting by the Associated Press)