The veteran lock became just the sixth player to earn a century of caps for the Pumas, but it was the visitors who drew first blood. Dewi Lake crossed from the back of a powerful driving maul.
The hosts wasted little time responding. Slick handling between Santiago Carreras and Mateo Carreras carved open the Welsh defence before Joaquin Oviedo powered over after Eddie James' initial intervention failed to halt the attack.
Argentina continued to build momentum, with Mateo Carreras and Rapetti repeatedly punching through attempted tackles as the home side carried with increasing authority.
Their growing dominance was rewarded again when Bautista Delguy brilliantly claimed a high attacking kick above Sam Costelow. The winger's aerial brilliance created the platform for Justo Piccardo, who shrugged off James' challenge before diving over in the corner.
Wales thought they had hit back through Jac Morgan after sustained pressure near the line, but the score was chalked off following a lengthy TMO review.
The setback did little to dent the visitors' resolve. Rhys Carre burrowed over from close range after another well-executed penalty move to keep Wales within touching distance.
Argentina, however, soon seized complete control. Although Morgan and James Botham combined to hold Oviedo up over the line, relentless pressure forced Wales into a string of penalties, eventually allowing Marcos Kremer to crash over from another driving maul.
Los Pumas finished the opening half in emphatic fashion. A slick attacking move ended with Santiago Carreras crossing for the bonus-point try, giving the hosts a commanding 28-14 advantage heading into the interval.
Argentina remained firmly in control in the second stanza as Oviedo grabbed his second try of the evening after bursting through the defensive line in the outside channel.
Substitute Matias Moroni was later denied a try because of a knock-on, while Wales reached two personal milestones. Hooker Ryan Elias earned his 50th Test cap after replacing the injured Lake, and flanker Kane James made his international debut when he came on for Aaron Wainwright.
James had barely settled before Wales grabbed another consolation, with replacement prop Ben Warren crashing over for his maiden Test try in only his second appearance.
The visitors enjoyed more possession during the closing stages, but Argentina's defence remained resolute as the Pumas comfortably saw out the contest to mark Petti's landmark occasion with an impressive victory.
Springbok star Ben-Jason Dixon immediately cast his eye to the challenge awaiting the Boks when they host Wales in Durban next week, predicting they were in for another tense tussle.
Argentina coach Lionel Scaloni was proud of the way his side dug deep to overcome Switzerland 3-1 after extra-time in their World Cup quarter-final clash on Saturday.
A much-changed Springbok team came through a slugfest with Scotland to eventually win 42-28 in their Nations Championship clash at Loftus Versfeld on Saturday.
Argentina left it late, but finally booked a FIFA World Cup semifinal date with England after a 3-1 victory in extra time over a spirited Switzerland in Kansas City on Saturday night.
