"Gabriel Batistuta has waited a long time for this World Cup, he did well and all the other forwards did well," Argentina midfielder Juan Sebastian Veron said.
Batistuta, 33, has scored 56 goals in 76 appearances for the national team, but after scoring the game's lone goal he was replaced with nine minutes left and was treated on the bench for an apparent right calf injury.
After not looking sharp early, Batistuta elevated above a group of players at the far post to reach Veron's corner and beat goalkeeper Ike Shorunmu to the short side.
Argentine coach Marcelo Bielsa was forced to choose between Batistuta and another world-class marksman, Hernan Crespo, to start at center forward.
Argentina had the better of the scoring chances throughout the match with Ariel Ortega, Juan Pablo Sorin and Batistuta having several opportunities. Ortega had a hard shot from outside the box deflected for a corner kick in the 30th minute, Sorin was denied twice from close range by Shorunmu after the break and Batistuta missed out on a pair of free kicks.
Argentina, one of the favorites to win the World Cup for the third time, also defeated Nigeria in 1994, when the sides were drawn into the same World Cup group in the United States.
Nigeria, with the youngest squad in the tournament, had trouble settling into the match early. Austin "Jay Jay" Okocha provided the team's best scoring chance after 32 minutes, when he tested goalkeeper Pablo Cavallero from 23 yards.
Forward Nwankwo Kanu fell awkardly and twisted his knee in the 11th minute and the Arsenal striker was replaced by Pius Ikedia.
It was a vital win for Argentina in what is the toughest group of the tournament. And when Sweden tied England later in the day, the Argentines found themselves alone at the top of the group.
"The match was quite hard," Vernon said. "We dominated much of the game, but it was a tough game.
"There is still a long way to go. We are still facing England and that is going to be a hard game."
Argentina and England will meet next Friday in Sapporo in what will be one of the most anticipated matches of the World Cup.
"I would have loved to have won the match, but we are talking about the standard of the game," Nigeria coach Adegboye said in praising Argentina. "I am very impressed.
"I am happy with my boys and I see this result as a challenge. We need to intensify our training to stay in the competition."