Cursed by the "Golden Generation" tag for their last two global tournaments, Belgium have been seen as underachievers given the wealth of talent at their disposal.
Tunisia hit back two minutes later with a Dylan Bronn header as Belgium's own sometimes shaky defending was exposed but another misplaced Tunisian pass enabled Thomas Meunier to feed his goal-hungry striker as Lukaku clipped in to make it 3-1 in stoppage time.
Belgium's Eden Hazard celebrates scoring their fourth goal.
Belgium were surging closer to a second, and it didn't take them long to get it as Lukaku steered home a pass from Dries Mertens just before 20 minutes.
Belgium has shown the most complete attacking force at the World Cup, though without yet playing a European or South American team.
Tunisia did manage a late consolation when Khazri swept home Hamdi Nagguez's cross but, unless Panama beat England, they will become the third African team to be eliminated, leaving Nigeria and Senegal to carry their continent's hopes in this competition.
Tunisia coach Nabil Maaloul said his young squad were nervous in their first appearance on the World Cup stage against England but they would be more confident against Belgium.
Lukaku doubled the lead for the Red Devils in the 16th minute with a low strike after going through on the left side of the box, 2-0.
After the comprehensive 3-0 victory over Panama in their first game, Belgium were always expected to be unchanged for the Tunisia match.
"'It's easy to play with a player like him", Hazard said after the win over Tunisia.
Against England on Thursday, Belgium will be favored to advance as the victor of Group H.
The Three Lions had all kinds of chances in the first half of that match, with some poor finishing and bad luck leading to the tense second half.