The Barcelona star provided the spark in a largely tense and evenly matched encounter at the Maracana, which ended with La Albiceleste having taken an early lead in Group F.
The Bosnians, meanwhile, will reflect on their dream World Cup debut having turned into a nightmare after just two minutes and eight seconds, when Sead Kolisinac scored the fastest own goal in the tournament's history.
In fairness, the Bosnia left-back had next to no time to react after Lionel Messi's free-kick was flicked on by Marcos Rojo, with the ball skidding off his shins and beyond the helpless Asmir Begovic.
The debutants, though, are made of stern stuff and refused to be demoralised by that sickening early blow. Within a few minutes, they were threatening an equaliser, with Sergio Romero called upon to race quickly and courageously from his line to save at the feet of the on-rushing Izet Hajrovic.
And though this game was not as open or incident-filled as most of those that have preceded it at Brazil 2014, Safet Susic's side went close again five minutes before the interval when Senad Lulic's powerful header forced Romero into another smart stop at his near post.
Argentina coach Alejandro Sabella had clearly seen enough to concern him, for he made a double half-time substitution, introducing both Gonzalo Higuain and Fernando Gago to the action.
It was, though, his starting forwards - Messi and Sergio Aguero - who combined forLa Albiceleste's next opportunity, with the latter blazing wildly over from the latter's clever through ball.
Messi had been fairly subdued in the first half but came to life again soon after when he jinked away from a couple of challenges and slid in Aguero for a shot that, on this occasion, forced Begovic into a solid save.
The Argentina captain would not be denied, though, and with 65 minutes scored an early contender for goal of the tournament. Bursting purposefully forward from midfield, he worked an incisive one-two with Higuain, skipped around Ermin Bicakcic and curled a perfect left-foot shot low into the net off the inside of Begovic's right-hand post.
The Maracana rose to salute a truly superb goal and, for Bosnia, there was no way back. Messi was now relishing the occasion and, having scored one and made another, he set about carving out a third, chipping through for Higuain, who sprang the offside trap only to head over.
However, the debutants did at least ensure a dramatic finale when Vedad Ibisevic raced through and squeezed a left-foot shot between the legs of Romero with five minutes remaining.
The damage had been done, though, and Susic's side will now hope to regain some ground in their remaining group matches against Iran and Nigeria.
Report courtesy: FIFA.com; Image: Wikimedia Commons