The Chelsea winger took just six minutes to break the deadlock from the penalty spot after he had been fouled by Syam Ben Youssef.
It meant that after a goal-laden start to the tournament there have now been 27 consecutive matches without a scoreless a draw, breaking a record which had stood since 1954 when the tournament was held in Switzerland.
Hazards former Chelsea teammate Romelu Lukaku got in on the act soon after as Belgium capitalised on their early advantage with a splendidly taken goal following a superb Dries Mertens pass.
Dylan Bronn briefly brought Tunisia back into the contest with a header but Lukaku put the match beyond doubt shortly before the interval with another adroit finish, clipping the ball over the advancing goalkeeper.
England struggled to break down the same opponents on Monday evening, but Belgium continued to find little difficulty in slicing Tunisia apart at will and Hazard struck again six minutes after the break, keeping his cool to round Farouk Ben Mustapha after expertly controlling a trademark Toby Alderweireld long pass.
Equally worryingly for England, both Hazard and Lukaku were withdrawn early in the second half to be given extra time to prepare for next Thursdays match in Kaliningrad which is likely to determine the winners of Group G.
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