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.
And Belgium, who wrap up Group G against England on Thursday, may confront fitness concerns with Lukaku, who had his right ankle worked on in the first half before coming off in the 59th minute with the result no longer in question.
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.
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Lukaku, meanwhile, doubled Belgium's lead in the 16th minute, scoring left-footed from the left channel after Dries Mertens forced a turnover.
That goal served to halt Belgium's early dominance, but they did grab a third with nearly the last kick of the half.
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.
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Thomas Meunier put him in behind the defence and Lukaku tucked his shot away, celebrating with De Bruyne, who started the move. Lukaku then ran ahead and, with Ben Mustapha drawn forward, Lukaku chipped it over the goalkeeper from nine yards out. Unless Panama beat England in Sunday's Group G match, Belgium will be through with a game to spare while Tunisia will be out.
Michy Batshuayi closed in on his first World Cup goal, but his attempt was cleared off the line after rounding Mustapha 14 minutes to full-time.
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