After racking up two wins and a goal difference of plus-six Belgium are virtually assured of advancing but it is not yet guaranteed - and they will be aware that they will need to tighten up at the back to handle the threat of the big guns deeper into the tournament.
The defeat means Tunisia, who have not won in the World Cup since 1978 - a run of 13 games - will exit the tournament if England pick up a point on Sunday against Panama. Hazard scored with a sixth-minute penalty kick he earned by being tripped, and Lukaku angled a low, left-foot shot into the corner of the opposing goal.
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.
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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. Farouk Ben Mustapha is expected to be his replacement.
Belgium and England clash next Thursday in their final Group G match in Kaliningrad in a contest likely to decide the pool victor.
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Yannick Carrasco came agonisingly close to adding a fifth goal when his whipped effort from outside the area fizzed agonisingly past the post, while substitute Batshuayi saw an effort cleared off the line by Yassine Meriah after he had rounded the goalkeeper.