Batshuayi finally got his goal for Belgium in the last minute of regulation time by finishing at the far post to make it 5-1 with a sweeping shot.
Chelsea forward Hazard's goal ensured that all of the first 27 matches in Russian Federation had at least one goal scored in them, beating the 64-year-old record of 26 matches set at the 1954 finals in Sweden, when every match had at least one goal.
The full-back's late challenge on Hazard was deemed, with the use of VAR, to have been just inside the area and the Chelsea man stepped up to crack the resulting spot-kick into the bottom-left corner.
Tunisia responded two minutes later when Dylan Bronn headed the ball past Thibaut Courtois at a free-kick.
With one eye on the England game, Martinez took off Lukaku, then Hazard as the half wore on and for the final 22 minutes brought on Batshuayi, who could have scored five.
Falleció el ex canciller Caputo
Será velado este miércoles a partir de las 16 y mañana a las 11 será enterrado en Jardín de Paz en Pilar. Vamos a extrañar su pensamiento y acción al servicio del país moderno y solidario que soñamos.
That gives Tunisia some reprieve as it must avoid defeat to retain any hope of qualifying for the knockout stages.
Belgium were aiming to firmly establish their World Cup credentials as they toook on Tunisia in Moscow.
Syam Ben Youssef needlessly crashed into Hazard to give away a sixth-minute penalty, which the captain calmly converted.
Belgium are ranked third in the world, behind only Germany and Brazil, but Martinez said there was no room for complacency against Tunisian, ranked 21.
Roberto Martinez's side opened their campaign with a 3-0 win over Panama, while Tunisia were beaten 2-1 by England thanks to Harry Kane's stoppage-time victor.
Tunisia have lost goalkeeper Mouez Hassen to injury after he damaged his shoulder in the defeat to England, per Goal's Michael Madyira. On Sunday, a draw for England against Panama would knock the African team out of the World Cup. After starting slow in a 3-0 win over Panama, Belgium got off to an incredibly fast start, scoring three times in the first half. Meanwhile, Tunisia has made one change Khaoui replaces Sliti in the playing eleven.