The Red Devils just need England to avoid defeat to Panama in Sunday's other Group G game to confirm their last-16 spot and no team at Russian Federation 2018 will want to be drawn against Roberto Martinez's side after this swashbuckling display.
Dylan Bronn headed one back for Tunisia in the 18th minute before Lukaku restored Belgian's two-goal lead in first-half stoppage 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 captain Wahbi Khazri got his team's second with nearly the last kick of the match.More news: Florida Man Charged With Murder In XXXTentacion’s Killing, Police Say
That goal served to halt Belgium's early dominance, but they did grab a third with nearly the last kick of the half.
Group G of the 2018 FIFA World Cup is really will take shape when Belgium and Tunisa meet.
It was 4-1 six minutes into the second half, as Hazard seized the initiative to get behind two defenders for an easy conversion after rounding Mustapha following a through pass from Toby Aldeweireld.
Hazard failed to turn home Lukaku's low cross from close-range soon after but the latter doubled the Red Devils' advantage after 16 minutes.
Only in the 90th minute, after Youri Tielemans found him in the box, did Batshuayi tally his first World Cup goal, and Khazri answered in the 93rd minute, moments before the full-time whistle.