Despite the junior Wallabies having been undefeated through the tournament with two wins and a draw, New Zealand lifted the title, relegating them to second place, after the Kiwis beat hosts South Africa in the final game at the same Nelson Mandela Bay Stadium in Gqeberha later on Sunday.
The Australians had earlier prevailed against Los Pumitas with six tries in total despite a fluctuating second half when the lead changed four times.
"Super proud of the boys," captain Eamon Doyle said afterwards.
"Coming in after last year finishing bottom of the table, with a draw and two wins, couldn't be happier or prouder."
Chris Whitaker's side scored after only three minutes as halfback James Martens reached out to score on the back of a rolling maul, and they increased the lead to 12-0 when winger Xavier Rubens went over in the left corner.
Argentine winger Aquiles Vieyra crashed over for their first score but after home flanker Pampa Storey got a yellow card for a dangerous tackle, No.8 Toby Brial scored to push the Australian lead out to 19-5.
Australia then conceded a penalty try and a yellow card to flyhalf Joe Dillon while attempting to stop a rolling maul and the Argentines were soon level as back-rower Agustin Garcia Campos dived over.
Soon after halftime, winger Shane Wilcox's try was answered by Vieyra's second but hooker Lipina Ata's pick-and-go put them back in front with 15 minutes left to play.
Victory was effectively sealed six minutes from time when the Aussies' sustained attack was eventually rewarded by a penalty try when their rolling maul was pulled down illegally.
Argentina grabbed a consolation try after the siren before the young Australians had to sit and watch in frustration as New Zealand overcame South Africa 48-45 to successfully defend their TRC U20 title.
But the Australians have laid down their marker before the Under 20 world championship in Italy in June and July.
