The Newcastle United midfielder captained La Albirroja and put his side ahead midway through the first half, netting with a neat low finish after taking advantage of a defensive error.
His second strike was a much more eye-catching one, though, as the 28-year-old cut inside and curled a terrific 20-yard effort into the top left-hand corner of the net with 49 minutes on the clock.
Tottenham Hotspur’s Son Heung-min reduced the deficit with 66 minutes gone and Almirón was withdrawn with quarter of an hour remaining, with Gabriel Avalos sent on in his place – meaning he wasn’t on the pitch to prevent Jung Woo-young from netting an injury-time equaliser to make it 2-2.
Almirón’s two goals were the fifth and sixth he has recorded in 41 outings for his country.
Santiago Muñoz's Mexico Under-21s, meanwhile, bowed out of the Maurice Revello Tournament after a semi-final defeat to hosts France on Thursday.
The United youngster started for his side at Stade Marcel Roustan in Salon-de Provence, but they found themselves three goals down by half time in their last-four clash after a brace from Sekou Mara and a strike from Lucien Agoume.
Efrain Alvarez pulled one back after the break but any faint hopes of a comeback were extinguished by Adil Aouchiche's late effort which made it 4-1 to Les Bleus.
Magpies forward Muñoz, who is on an 18-month loan at St. James' Park, played the full 90 minutes for Mexico, who exit the competition at the hands of the favourites.
Elsewhere, Jeff Hendrick completed the full game for the Republic of Ireland as they suffered a 1-0 UEFA Nations League defeat to Ukraine on Wednesday, with Viktor Tsyhankov netting the only goal of the contest at the Aviva Stadium in Dublin.
Chris Wood was in international action too, entering the fray as a 78th-minute substitute in New Zealand's 0-0 friendly draw with Oman at the Education City Stadium in Doha.
However, suspension kept United defenders Fabian Schär and Emil Krafth out of Switzerland and Sweden's Nations League fixtures against Spain and Serbia respectively.
