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.
Should they lose their final game against England, now on three, and pointless Panama somehow beat England and Tunisia, all three would have six points and the top two would be decided on goal difference.
Wahbi Khazri found a second consolation for the Tunisians after steering home a cross-field pass a minute from time.
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The goal means Lukaku became only the fifth Belgium player to score in back-to-back World Cup matches, with Marc Wilmots the last to do it when he scored in every group-stage game in 2002.
Belgium can take a big stride towards the last 16 with a win over Tunisia.
With half-time approaching, the Belgians grabbed their third goal.
Toby Alderweireld's long pass from defence was taken on the chest by Hazard, who then rounded Mustapha to stroke into an empty net.
Yannick Carrasco came agonisingly close to adding a fifth goal when his whipped effort from outside the area fizzed agonisingly past the post, while substitute Batshuayi saw an effort cleared off the line by Yassine Meriah after he had rounded the goalkeeper.