Belgium attacked from the off and needed only five minutes to take the lead, when Hazard was barged over by Syam Ben Youssef just inside the box and got up to send Tunisia keeper Farouk Ben Mustapha the wrong way from the spot.
Lukaku gave the Red Devils breathing space once more with a dinked finish from a Thomas Meunier pass just before half-time.
Hazard added his second goal soon after the break, racing on to a precise Toby Alderweireld pass and rounding the keeper to fire home.
Substitute Michy Batshuayi, who also had a shot cleared off the line and hit the bar from close range, finally found the target from Youri Tielemans’ cross.
The North African side, needing a win to reignite their own hopes of progress, gave themselves hope when Dylan Bronn got on the end of Wahbi Khazri’s whipped free-kick just 109 seconds later.