Eden Hazard struck twice, in either halves, while Lukaku had both of his goals in the first half itself.
Cursed by the "Golden Generation" tag for their last two worldwide tournaments, Belgium have been seen as underachievers given the wealth of talent at their disposal. Khazri and Dylan Broon scored for Tunisia but it was not enough as they were eliminated from the tournament.
The United player now has four goals at Russian Federation 2018, making him joint top scorer alongside Portugal's Cristiano Ronaldo.
And Belgium, who wrap up Group G against England on Thursday, may confront fitness concerns with Lukaku, who had his right ankle worked on in the first half before coming off in the 59th minute with the result no longer in question.
And Hazard doubled his total in the 51st minute, scoring on an open net after he ran under a pass from Toby Alderweireld and worked his way around goalkeeper Farouk Ben Mustapha before finishing.
Roberto Martinez's star-studded squad emerged as 3-0 winners in their opening Group G game in Sochi on Monday but will likely find Tunisia a far more robust and defensively astute opponent when they meet at the Spartak Stadium in Moscow. In that case Tunisia would be eliminated on zero points.
Belgium moved to the brink of the World Cup knockout rounds on Saturday.
"Give huge credit to Tunisia, they wanted to win from the beginning, they pressed high up, they were happy to leave space and the credit we deserve is that we used that space well".
Barring major upsets, the 28 June tie against Gareth Southgate's men in Kaliningrad will decide who tops the group and Martinez was wary of England's threat.
"I felt something in my calf in the first half but nothing big and I think I will be OK tomorrow", said Hazard.