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That made sure of the points, but Belgium were not finished yet.
However, Tunisia will not make life easy for Belgium as they seek to provide a bright spot in a poor World Cup for African sides, with Egypt and Morocco already out.
The Carthage Eagles put themselves back in the swing of things courtesy of Dylan Brodman, who headed home from a free-kick with their first shot on goal.
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.
Coffins at DMZ to collect USA service members' remains from North Korea
Trump's remarks about the remains on June 20 were part of a broader description of progress made in North Korea. "That's OK. At the summit, Kim committed to "complete denuclearization of the Korean Peninsula", but no details were worked out.
The Manchester City midfielder picked out Hazard from his own box, sent a long pass that pierced through the Tunisian rearguard, and the Chelsea forward did the rest by rounding Farouk Ben Mustapha and slotting into the empty net. The past mark was 26 games without a 0-0 draw from the 1954 tournament.
Despite cruising to a routine 3-0 victory over Panama in their Group G opener, there were still one or two niggling doubts regarding Roberto Martinez's style of play despite the obvious talent at his disposal.
Frank Lampard had plenty to say about England's chances against Belgium and despite the impressive nature of the Tunisia win, he was feeling pretty confident.
"The World Cup does not respect generations, the World Cup doesn't respect individual names, it only respects winning teams", he said.
Belgium have closed in on a spot in the last 16 with a magnificent 5-2 win over Tunisia in their Group G encounter in Moscow.
The 25-year-old's fourth goal of the tournament saw him break Jan Ceulemans's record for the most goals scored by a Belgian at major tournaments.