Tunisia, meanwhile, valiantly held England to what appeared to be a draw, but a late Harry Kane header snatched away the point from the Eagles of Carthage, who find themselves in a tough spot fighting for their tournament survival.
Romelu Lukaku scored after 16 minutes and though Dylan Bronn pulled one back for Tunisia, Lukaku made it 3-1 just before half-time.
Hazard scored the opener on a sixth-minute penalty, converting after he was taken down just inside the right of the area by Syam Ben Youssef.
Tunisia coach Nabil Maaloul swapped his goalkeeper with Farouk Mustapha taking over from Mouez Hassen, who played in the opening 2-1 defeat to England, failing to stop Harry Kane scoring the late victor for the Three Lions.
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That goal served to halt Belgium's early dominance, but they did grab a third with nearly the last kick of the half.
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.
Toby Alderweireld's long pass from defence was taken on the chest by Hazard, who then rounded Mustapha to stroke into an empty net.
Tunisia captain Wahbi Khazri got his team's second with nearly the last kick of the match. Unless Panama beat England in Sunday's Group G match, Belgium will be through with a game to spare while Tunisia will be out. Belgium were generally on cruise-control for the final half hour, though the North Africans had the last word as Wahbi Khazri scored in stoppage time.