Captain Baptiste Serin as well as debutants Antoine Frisch and Theo Attissogbe crossed for tries for Les Bleus, who were without star scrum-half Antoine Dupont as he prepares to play sevens at the Paris Olympics.
Replacement centre Matias Orlando was Los Pumas' only try-scorer as former fly-half Contepomi tasted defeat having taken over from Michael Cheika after last year's Rugby World Cup where Argentina lost to England in the third-place play-off.
"We ticked a lot of boxes which allowed us to win the game," Galthie told Canal+.
"Not everything was perfect, we can improve a few things, I think we can play with a bit more freedom.
"You can consider this a great match from us," he added.
Contepomi made nine changes from their last game, October’s World Cup play-off, but was still able to name an experienced team including flanker Pablo Matera winning his 99th cap.
Galthie handed debuts to seven players in his starting lineup including Montpellier flanker Lenni Nouchi, who was called into the side on Friday to replace the sick Judicael Cancoriet.
The most experienced member of Galthie's squad was skipper and Dupont’s stand-in Serin, making his 45th Test appearance eight years on from his international debut in Argentina, Les Bleus’ last defeat to the hosts.
After a sluggish first 20 minutes for both sides Les Bleus' fly-half Antoine Hastoy opened the scoring with a penalty goal.
Argentina drew level three minutes later as Santiago Carreras, who was Los Pumas’ first-choice outside-half at the World Cup, slotted a penalty.
Just before the half-hour mark Argentina came within inches of scoring the opening try but France's debutant centre Frisch stopped winger Bautista Delguy from grounding the ball with a superb last-gasp tackle in the left-hand corner.
Impressive Frisch
The visitors ended the half the best and took control of the game as a sublime solo try from 30-year-old Serin, which included a 40m break, followed a powerful France scrum deep in Argentina territory.
Hastoy added the conversion to make it 10-3 as Les Bleus eyed a fifth straight win over Argentina.
Just five minutes after the break, France extended their lead as an impressive Frisch, who turned 28 on Monday, charged over and Hastoy’s extra took the score to 17-3.
With 20 minutes to go France’s lead was cut to 20-8 as Pumas captain Julian Montoya crashed over after La Rochelle’s Hastoy had kicked a second penalty.
Any hopes of an Argentina comeback were dashed with 13 minutes left as France winger Attissogbe celebrated his own Test debut with a try.
The Pau flyer smashed through three would-be defenders and took the score to 25-8.
With three minutes left Argentina claimed a consolation try through Orlando.
The sides meet again on Saturday in Buenos Aires, four days after a France team taken from the wider travelling squad face Uruguay in a non-Test match in Montevideo.
