With Argentina forced into a late reshuffle after Roberto Ayala was forced to withdraw, the onus was on stand-in captain Juan Sebastian Veron to stamp his mark on the game.
And despite playing in his preferred position in the centre of midfield, the Manchester United man made his best contributions from the flanks early on.
Argentina enjoyed the majority of the possession, yet were unable to convert it into a comparable number of chances.
As the first half unravelled, the goalkeepers were to the fore.
Nigeria's Shorunmu made a good finger-tip save to divert a fierce drive from the lively Ariel Ortega.
At the other end, Nigeria's star player Jay-Jay Okocha went closest to opening the scoring with a superb left-foot strike.
But Argentina keeper Pablo Cavallero was equal to it, producing a stunning save to push the ball over the crossbar.
After the interval, Argentina brought on Kily Gonzalez for Claudio Lopez and Bielsa's men certainly looked more threatening.
But for the profligacy of Batistuta, who had missed an earlier chance to head his side in front, the South Americans should have taken the lead on 48 minutes.
Batistuta somehow contrived to volley wide when unmarked in the Nigeria area.
Juan Pablo Sorin and Mauricio Pochettino also went close with headed efforts that came courtesy of Veron's right foot.
Argentina's pressure eventually paid dividends when Batistuta converted his most difficult opportunity with unerring ease, rising at the far post to power in a header.
Batistuta almost netted a second, but his powerful free-kick from well outside the area was scrambled away by Shorunmu.
Such was their supremacy, Argentina were able to replace Veron and Batistuta with Pablo Aimar and Hernan Crespo late on in the game.
Gonzalez should have scored in the dying seconds but again Shorunmu saved brilliantly.
Argentina ended the game very much in the ascendancy.
And on this performance they will prove tough opponents for England and Sweden in group games to come.
Argentina: Cavallero, Placente, Sorin, Pocchettino, Samuel, Zanetti, Simeone, Veron (Aimar 78), Ortega,
Claudio Lopez (Gonzalez 45), Batistuta (Crespo 81).
Subs Not Used: Almeyda, Bonano, Burgos, Caniggia, Chamot, Gallardo, Husain, Gustavo Lopez, Ayala.
Booked: Samuel, Simeone.
Goal: Batistuta 63.
Nigeria: Shorunmu, Yobo, Babayaro, Okoronkwo, West, Sodje (Christopher 73), Ogbeche, Okocha, Lawal,
Kanu (Ikedia 48), Aghahowa.
Subs Not Used: Adepoju, Afolabi, Akwuegbu, Ejide, Ejiofor,
Enyeama, Obiorah, Opabunmi, Udeze, Utaka.
Referee: Giles Veissiere (France).