The title also allowed the South Americans to match their best gold haul at a Games of three which was last achieved in 1948.
“It’s like touching the sky with your hands, so I feel so happy,” said Gonzalo Peillat, who scored one of the goals to take his tally for the Games to 11.
“We won the tournament and it was the first time in the history of Argentina.
“It’s my dream. When I started playing hockey I always was thinking about this dream and now it came true.”
Belgium, also playing in their first final, had taken the lead after just three minutes through Tanguy Cosyns.
But the South Americans hit back with Pedro Ibarra, Ignacio Ortiz and Peillat scoring in quick succession in the first quarter.
Gauthier Boccard hit a sensational second for Belgium when he dribbled the ball past three defenders before finding the corner of the goal.
But Augustin Mazzilli guaranteed the gold when he was allowed to tap into an empty net.
“I think maybe it’s going to help a lot in men’s hockey in Argentina,” said Mazzilli.
“The women’s team did everything really, really good the whole time (they won four gold medals).
“So we need now to increase our level in hockey in men’s so I hope everyone is watching this and we can play with more payers in Argentina.”
In an interesting twist, the Argentine squad featured the grandson of Belgian cycling legend Eddie Merckx although Luca Masso played just six minutes of the final.
Belgium’s New Zealander coach Shane McLeod said his team made too many errors at crucial times.
“I think later on we’ll reflect a bit more and be very proud of what we’ve done but you always wanna win that last game and we just did too many things wrong today,” he said.
“It’s a pity. That’s sport.”
The result was still Belgium’s best finish in men’s hockey at an Olympics, with third place at the Antwerp Games in 1920 their previous best.
Earlier, two-time defending champions Germany beat the Netherlands in a shootout for bronze after they finished level at 1-1 at the end of normal time.
The bronze was particularly pleasing for Mats Grambusch who was playing alongside his brother Tom.
“To get an Olympic medal is probably one of the biggest things in the world, and getting a medal with your brother is indescribable,” said Mats.