However, Lionel Messi capped an improved display in the second half with a spectacular goal from 20 yards, and although Vedad Ibisevic managed to halve the deficit with five minutes remaining, Argentina held on for the three points.
Below, Sports Mole assesses whether Argentina were deserving of the three points.
On target: 2
On target: 6
Was the result fair?
While Bosnia deserve a lot of credit for their performance in Rio de Janeiro, Argentina just about deserved the three points. La Albiceleste, who were one of the pre-tournament favourites, have a lot of pressure on their shoulders, and while they struggled for the opening hour of this contest, they displayed plenty of encouraging signs during the final 30 minutes. However, while Bosnia will be disappointed with the result, they can take plenty of positives into their match with Nigeria at the weekend.
Argentina are accustomed to playing with three at the back, but from the offset, it was clear that it wasn't going to be effective against a well-drilled Bosnia outfit. They were unable to create any kind of fluidity through the middle, and their narrow formation often resulted in Bosnia taking advantage down the flanks.
Despite continuing to look below-par, they looked much more comfortable with a back four and three in attack, and Messi was able to have a greater impact on the match when operating in tandem with two teammates rather than just Sergio Aguero. World Cup winners rarely begin with a five-star performance, and Argentina will need to improve if they are to have a shot at reaching the latter stages.
There were fears that Bosnia, who were making their World Cup debut, could be overawed by the occasion, but if anything, they relished the opportunity to compete in front of what was effectively a home crowd. While no-one stood out, they found the right balance between defence and attack, and for a time, it stifled their more illustrious opponents.
They will be disappointed that they couldn't make more of a number of situations in the final third, but they can take the positive that they gave Argentina a game tonight, and on another evening, they would have nicked a point. They have every reason to fancy their chances against Nigeria at the weekend.
Sports Mole's man of the match
Lionel Messi: With none of the players on show at the Maracana standing out, the man of the match award can only go to Messi. The Argentina skipper provided an assist for the first goal and scored a goal out of nothing for the second. It was an average performance from a man who is driven to make his mark at a World Cup finals, but his contribution ultimately proved to be the difference between the two teams.
While he has every reason to count himself unlucky, Kolasinac must go down as producing the biggest gaffe over the course of the 90 minutes. The 20-year-old Schalke 04 defender had little chance to avoid making contact with the ball at the back post, but if we were to be ultra critical, he could have possibly found a way to divert the ball behind for a corner rather than into his own net.
Salvadoran referee Joel Aguilar got through his night's work without the need to make any game-changing decisions. The officials in Brazil haven't covered themselves in glory but this was one of the better performances of the tournament. Aguilar was also wise to some of the theatrics from both sides, which can only be a good thing as this competition progresses.
Argentina: Argentina have the opportunity to secure their place in the second round when they play Iran in the early kickoff on Saturday.
Bosnia-Herzegovina: Bosnia will attempt to hit back from tonight's defeat when they face Nigeria on Saturday evening, in a game which could potentially decide who qualifies behind Argentina.