"Nadalcaraz", as the Spaniards have called themselves, produced some spectacular tennis as they were roared to victory by a packed evening crowd on Court Philippe Chatrier.
Despite some injury worries, Nadal looked sharp as the 14-time French Open champion sealed the opening set with a fierce backhand winner.
The Mallorcan, who has previously won two gold medals in singles, is now considering focusing on doubles.
"We are going to make the decisions that we think are most appropriate as a team to try to have the best chances of bringing medals home for the Spanish team, to try to give ourselves the chances of that happening," Nadal said.
"Sometimes more is more, sometimes more is less, but with that I'm not saying that I'm not going to play at all," he added.
Alcaraz, winner of this year's French Open and Wimbledon titles and the new force in men's tennis, appeared to be loving life alongside his idol.
"His energy, the way that he handled the difficult moments was unbelievable. And obviously I tried to learn from him," Alcaraz said.
While the Argentines showed experience as a pair, the Spaniards sometimes struggled to find their marks, recording 15 unforced errors in the first set, mainly by Alcaraz, against four for their opponents.
Gonzalez and Molteni opened up the second set with a 3-0 lead including a break but the Spaniards got back on the scoreboard as they seemed to move into the groove, returning more precise volleys and hitting some cracking shots.
After breaking at 4-4, Nadal put away a smash to bring up match point in the next game as the crowd chanted "Rafa, Rafa" and the Spaniards sealed the win with an Alcaraz volley - the crowd rising as one to give the duo a standing ovation.
The Spanish pair will play the winners of the match between the Netherlands' Tallon Griekspoor and Wesley Koolhof and Hungary's Marton Fucsovics and Fabian Marozsan, which was postponed to Sunday due to rain.
