Defeat for Tunisia leaves them all-but-out of the tournament, needing Panama to defeat England on Sunday to maintain even the smallest shred of hope of reaching the knockout rounds.
Romelu Lukaku scored just before halftime to give Belgium a 3-1 lead over Tunisia and equal Cristiano Ronaldo's tally of four goals so far at the World Cup.
Hazard tucked away the penalty to hand Belgium a lead that was soon doubled by Lukaku, who converted a Dries Mertens pass with an accurate, low, left-footed shot.
Group G of the 2018 FIFA World Cup is really will take shape when Belgium and Tunisa meet.
"We had to suffer in spells but when we were in full flow going forward, we look really sharp".
Belgium were much the better team, looking risky on nearly every attack, but they were seriously aided and abetted by some ragged defending and non-existing marking from their opponents.
Things quickly got worse for Tunisia when Ali Maaloul's heavy touch on the halfway line allowed Dries Mertens to nip in and release Lukaku, who found a flawless low finish.
Tunisia were not down and down and punched back nearly instantly in front of raucous support in Moscow when Dylan Bronn, who plays his club football for Gent in Belgium, headed home from a whipped free-kick from Wahbi Khazri to pull one back.
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.
Substitute Michy Batshuayi made it a rout in stoppage time, and failed with three other good scoring chances. Coach Nabil Maaloul has worked on correcting the mistakes against England and the target is to win against the Belgians. "We would like to apologise to the Tunisian fans".