His pace surprised Ben Youssef, who mistakenly upended his opponent, the referee quickly pointing to the penalty spot.
Lukaku also scored two goals in Belgium's opening 3-0 win over Panama.
Following his double against Panama it took the him to four goals for the tournament, level with Portugal's Cristiano Ronaldo, and made him Belgium's highest scorer at a single World Cup - after one-and-a-half games.
And Lukaku also became the first player to equal Maradona's 1986 World Cup feat of back-to-back braces. The past mark was 26 games without a 0-0 draw from the 1954 tournament.
Belgium against Tunisia was full of stats.
Tunisia responded two minutes later when Dylan Bronn headed the ball past Thibaut Courtois at a free-kick. With seven defeats in seven matches for Arab countries, Tunisia will hope to stop the rot.
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.
Against Tunisia, they were up against a side that frustrated England for large parts of their encounter last weekend, and could probably count themselves unlucky to come away with nothing after Harry Kane's late victor. Martinez has kept faith with a defensive line of three, with Dedryck Boyata in the centre flanked by Tottenham Hotspur pair Toby Alderweireld and Jan Vertonghen.
That would leave their meeting in Kaliningrad on Thursday to decide who tops the group and it is Belgium who now hold the upper hand there, with their sparkling finishing in the sunshine at the Spartak Stadium leaving their goal difference significantly better off.
Since then most editions of the tournament have averaged between 2 and 3 goals per game.