England, meanwhile, would seal their own qualification for the last 16 by beating Panama.
Syam Ben Youssef needlessly crashed into Hazard to give away a sixth-minute penalty, which he calmly converted.
Tunisia captain Wahbi Khazri got his team's second with nearly the last kick of the match.
However, Tunisia will not make life easy for Belgium as they seek to provide a bright spot in a poor World Cup for African sides, with Egypt and Morocco already out. VAR was used, confirming that the challenge was illegal and that it had taken place just inside the penalty area.
With the last touch of the half, Lukaku reimbursed their two-goal advantage with a deft chip over an advancing Ben Mustapha.
Khazri's inswinging free-kick from the left was met by Bronn, who flashed a header past Thibaut Courtois entirely against the run of play.
With half-time approaching, the Belgians grabbed their third goal.
Tunisia have lost goalkeeper Mouez Hassen to injury after he damaged his shoulder in the defeat to England, per Goal's Michael Madyira.
An inch-perfect Kevin de Bruyne pass sent Hazard clear for his second six minutes after the restart, the midfielder showing superb balance and skill to round keeper Farouk Ben Mustapha and tuck home to effectively end the contest.
With the game essentially wrapped up, Martinez opted to bring Lukaku off before the hour, the striker having picked up a knock on his foot earlier in the game.
Batshuayi looked like he would endure a miserable afternoon after two more missed opportunities - one crashing back off the crossbar from close-range - but the Chelsea man finally scored late on, meeting Youri Tielemans' fine cross at the back post with a controlled half-volley.