Joachim Low's men struggled to break down the stubborn hosts for the first third of the match, but after a quick-fire double before half-time the visitors cruised to a win.
The Barcelona star was left on the bench after missing training on Thursday but the Albiceleste were still comfortable winners on Saturday.
The striker scooped the ball over the goalkeeper in the opening half to net his first international goal and secure the three points for Vicente del Bosque's men.
Oscar and Luiz Gustavo scored either side of the Barcelona star after Raphael Varane had put the home side ahead.
Marco Reus fired the home side ahead before Mile Jedinak and James Troisi reversed the scoreline, but the Inter forward pulled Joachim Low's men level.