The victory leaves the Red Devils top of Group G with two wins ahead of their clash on Thursday against England, who play Panama on Sunday.
After also scoring twice in the opening 3-0 win against Panama, Manchester United's Lukaku showed clinical finishing with two first-half goals in Moscow, matching Ronaldo's tally in Russia.
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Not to be outdone, Belgium captain Eden Hazard scored in either half, including an early penalty at the Spartak Stadium, before substitute Michy Batshuayi added their fifth.
Tunisia's consolation goals came from defender Dylan Bronn and captain Wahbi Khazri.
The Belgians were criticised by coach Roberto Martinez for starting slowly against Panama in their first group match but flew out of the blocks in Moscow.
Hazard, having been on the receiving end of some bruising tackles in Belgium's opener, was sent tumbling after just five minutes but converted the penalty to open his Russian account.
Midfielder Ferjani Sassi picked up an early booking for complaining when Tunisia's appeals for a penalty fell on deaf ears, just before Belgium added their second goal.
Ali Maaloul's weak pass on the halfway line was collected by Dries Mertens, who sprinted away and put Lukaku clear.
The striker coolly hit his shot inside the far post, just past the outstretched glove of Tunisia keeper Farouk Ben Mustapha, in the 16th minute.
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Tunisia responded two minutes later, Bronn leaping highest to head home a free-kick from his skipper Khazri on 18 minutes, only to be later carried off after landing awkwardly following a collision.
With half-time approaching, the Belgians grabbed their third goal.
After earlier squandering two clear chances created by Kevin De Bruyne, Lukaku converted his third opportunity just before the half-time whistle.
Thomas Meunier put him in behind the defence and Lukaku tucked his shot away, celebrating with De Bruyne, who started the move.
The Manchester City midfield maestro turned provider again after the break for Hazard.
The Chelsea star sprinted onto De Bruyne's lofted pass, held off two defenders, rounded keeper Ben Mustapha and tapped home Belgium's fourth goal in the 51st minute.
With one eye on the England game, Martinez took off Lukaku, then Hazard as the half wore on and for the final 22 minutes brought on Batshuayi, who could have scored five.
The Borussia Dortmund forward had a chance cleared off the line, was twice denied by Ben Mustapha's saves and hit the crossbar, finally converting a cross for Belgium's fifth goal.
Tunisia captain Khazri grabbed their second goal just before the final whistle of their second defeat in Russia.
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