Hazard and Lukaku completed their doubles within the first 51 minutes of the Group G fixture and Michy Batshuayi added a fifth for his side in the final minute to all but secure Belgium's place in the last 16 of the competition.
Belgium started the match on the front foot and it took just five minutes for the Red Devils to win a penalty after Hazard was tripped inside the penalty area, with the Chelsea playmaker getting to his feet to sweep the ball to the right of Farouk Ben Mustapha.
Hazard should have added a second soon afterwards but scuffed a shot towards goal from 12 yards, but Lukaku soon doubled his side's advantage after latching onto a Dries Mertens pass before finding the far bottom corner from inside the penalty area.
However, Tunisia quickly halved the deficit through Bronn, who was perfectly placed to head into the far corner after Khazri had delivered a teasing inswinging cross.
Belgium responded through speculative efforts from Yannick Carrasco and Toby Alderweireld, but the tempo of the game was broken up after Bronn was stretchered off with what appeared to be a knee injury.
Tunisia improved as the first half progressed with Ferjani Sassi dragging a shot wide of Thibaut Courtois's right post and Khazri forcing the Chelsea stopper to tip his long-range attempt over the crossbar.
Fakhreddine Ben Youssef also went close with a volley from the edge of the area, but all of Tunisia's hard work was undone just before the break as Lukaku scored his second.
Both teams returned for the second half with the intention of going on the attack but Belgium soon put the game beyond any doubt with a fourth goal as Hazard collected a pinpoint pass from De Bruyne before rounding Ben Mustapha and volleying into an empty net.
To their credit, Tunisia continued to press forward in search of goals but the better chances were falling to Belgium with Carrasco curling agonisingly wide of the far top corner.
Anice Badri had Tunisia's best attempt with the forward's low effort being claimed by Courtois but Belgium - after witdrawing both Lukaku and Hazard - dominated the final quarter of the game.
Batshuayi had several chances to score soon after his introduction, with his first opportunity coming after rounding Ben Mustapha but his resulting shot was cleared off the line by Yassine Meriah.
The Chelsea forward then lashed the ball against the crossbar from six yards after Ben Mustapha had fumbled Carrasco's low effort, before the substitute was denied by the goalkeeper from point-blank range after making a solid connection with a volley.
However, Batshuayi would finally hit the back of the net in the final minute of normal time, sliding in to volley into the far corner after a teasing cross from Youri Tielemans.
In the third minute of added-on time, Tunisia netted a second through Khazri - who swept into the far corner from close range - but Belgium were full value for their win and this performance has laid down a marker to England and their tournament rivals.
BELGIUM (3-4-3) Courtois; Alderweireld, Boyata, Vertonghen; Meunier, De Bruyne, Witsel, Carrasco; Mertens (Tielemans 86'), Lukaku (Fellaini 59'), Hazard (Batshuayi 68')
TUNISIA (4-3-3): Ben Mustapha; Meriah, S.Ben Youssef (Benalouane 41'), Bronn (Nagguez 24'), Maaloul; Sassi (Sliti 59'), Skhiri, Badri; F.Ben Youssef, Khazri, Khaoui