It was from a Messi corner that full-back Nicolas Otamendi headed in the game's only goal on the 67th minute. Argentina coach Alejandro Sabella rushed out from the dug-out to hug his team and savour the win in his first match in charge of the two-time FIFA World Cup™ winners.
Messi came close to scoring twice in an entertaining first-half, while Angel Di Maria failed to convert a fine pass from Messi in the ninth minute despite having only Venezuela goalkeeper Rafael Romo to beat.
Venezuela proved more of a threat after the break, with Sergio Romero forced into action to deny Cesar Gonzalez.
That helped ease the anxiety of Sabella, who was looking to get off to a good start after replacing Sergio Batista as coach in the wake of Argentina's disappointing performance at the Copa America on home soil in July.
The 14-time Copa winners were knocked out on penalties in the quarter-finals by Uruguay, triggering a wave of criticism with fans desperate to see their team break an 18-year title drought.
Venezuela, on the other hand, were fresh from reaching the semi-finals of the Copa America for the first time but they failed to capitalise on the chances that came their way.
Argentina, hoping to build up a loyal following across southern Asia, now head to the Bangladeshi capital Dhaka for another friendly with Nigeria on 6 September.