Tournament debutants Panama deservedly made it to half time unscathed, but Belgium's world-class talent showed with a flurry of high-quality goals in the second period.
An eye-catching volley from Dries Mertens ended Panama's resistance two minutes after the restart, and Manchester United striker Lukaku followed with two tidy finishes of his own to make the scoreline more convincing.
Roberto Martinez's side were quick out of the blocks and forced two early saves out of veteran Panama goalkeeper Jaime Penedo, who kept out Yannick Carrasco and Mertens to prevent his side from suffering a nightmare start.
Defender Roman Torres scored the goal which booked Panama's ticket to Russia but the defender nearly lost his national hero status when his short back-pass gifted Eden Hazard a golden opportunity which he failed to convert from a tight angle on 12 minutes.
Belgium's chances became more infrequent as the half developed and the minnows began to grow into the grand occasion, although Mertens did shoot into the side-netting, and Hazard called Penedo into action once again following a burst of pace into the box.
The Central Americans did not pose much of an attacking threat, but by the time that Armando Cooper fired over from 25 yards on 44 minutes, they had at least managed to quell the danger coming from their star-studded opponents.
That was until Mertens relieved the pressure growing on the Red Devils with a skilful volley on 47 minutes, instinctively lifting the ball over Penedo and inside the far post after Panama had squandered several chances to clear.
Panama's best chance to equalise came eight minutes later when makeshift wing-back Carrasco switched off from his defensive duties to allow Michael Murillo a one-on-one that was saved by Thibaut Courtois.
Two goals in six minutes from Lukaku then settled proceedings, firstly steering in a 69th-minute header that was supplied by an outside-of-the-boot cross from Kevin De Bruyne.
Another of Belgium's Premier League stars provided Lukaku with his second as Chelsea playmaker Hazard burst forward on the counter and released the 25-year-old for a deft chip over Penedo - his 38th international goal in 70 caps.
Belgium take their place at the top of Group G ahead of England's opening game against Tunisia.
BELGIUM (3-4-2-1): Courtois; Alderweireld, Boyata, Vertonghen; Meunier, De Bruyne, Witsel (Chadli, 90'), Carrasco (Dembele, 76'); Mertens (T Hazard, 83'), Lukaku, E. Hazard
PANAMA (4-1-4-1): Penedo; Murillo, Escobar, R. Torres, Davis; Gomez; Godoy, Cooper, Barcenas (G Torres, 63'), Rodriguez (Diaz, 63'); Perez (Tejada, 73')