Beaten finalists four years ago in Brazil, Argentina struggled in the qualifiers, only securing their ticket with a win in their final match, but they were far too strong for a Haiti side 103 places below them in the FIFA rankings.
Lionel Messi took on his usual role as the star of the show, scoring a hat-trick and setting up the fourth for Sergio Aguero, who came off the bench to combine well with the Barcelona striker and Christian Pavon, another second half substitute.
Messi opened the scoring from the penalty spot after 17 minutes before doubling Argentina's lead 12 minutes into the second half with a simple tap-in after the keeper could only parry a header.
He scored his third after 65 minutes and set up Aguero two minutes later to slot home a fourth as Argentina ran amok at Boca Juniors' home stadium in the country's capital.
Peru, meanwhile, out-thought, outplayed and out-muscled an understrength Scotland, who rarely threatened at the Estadio Nacional in a rematch of a famous 1978 World Cup encounter between the sides that the South Americans won 3-1.
Christian Cueva put Peru 1-0 ahead after 36 minutes from the penalty spot before Jefferson Farfan took advantage of slack defending just seconds after the break to complete the scoring.
The victory was Peru's third in a row against European opposition following friendly wins over Croatia and Iceland, and fills them with optimism as they head to their first World Cup since 1982.
"Peru is ready to face any team in the world," Peru coach Ricardo Gareca told reporters. "This team is prepared to resolve problems that come our way."
Peru are now unbeaten in 13 games but have been drawn in one of the most difficult pools in Russia, alongside France, Denmark and Australia in Group C.
Argentina, meanwhile, are in Group D with Iceland, Croatia and Nigeria.
In another game in Panama City, the hosts prepared for their first ever World Cup with a 0-0 draw against Northern Ireland.
Panama, who are in Group G with England, Belgium and Tunisia, have one final friendly against Norway in Oslo scheduled for next week.
Argentina play Israel before heading to Russia and Peru face fellow finalists Sweden in Gothenburg.
(Reporting by Andrew Downie; Editing by John O'Brien)
