Hazard won and converted a sixth minute penalty before Lukaku ran onto a Dries Mertens pass to coolly slot home the second 10 minutes later.
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.
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He scored twice in Belgium's 3-0 opening Group G game against Panama and needed just 45 minutes against Tunisia to score another double.
Tunisia captain Khazri grabbed their second goal just before the final whistle of their second defeat in Russian Federation.
Belgium can take a big stride towards the last 16 with a win over Tunisia.
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Lukaku clipped a right-foot shot over advancing goalkeeper Farouk Ben Mustapha to match Cristiano Ronaldo with four goals as the tournament's top scorers.
Any thoughts that the rampant Belgians would accelerate out of sight were dispelled - at least briefly - just two minutes later, though.
Lukaku, though, came through in added time with the third goal, moments after Kevin De Bruyne missed the striker in the box by mere inches. Tunisia pull a goal back.
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.
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. 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.