The Pumas scored four tries – two in the opening ten minutes – to help open up a 17-0 lead, and two more in the final 11 minutes when the Irish were taking risks.
Juan Imhoff crossed either side of half-time, while centre Matias Moroni and full-back Joaquin Tuculet scored the other tries for Argentina.
The Irish will rue their slow start and the absence of key elements of their leadership group in captain Paul O’Connell, star stand-off Johnny Sexton and flankers Sean O’Brien and Peter O’Mahony, who were either injured or suspended.
“It was a fantastic Argentina performance and a performance our players will learn from,” Ireland coach Joe Schmidt said. “There’s a lot of my players who have never been in a match of that intensity.”
Four seasons playing the southern hemisphere Rugby Championship have proved invaluable for the Pumas.
“Since 2012, the growth of our rugby has been enormous,” Argentina coach Daniel Hourcade said. “We started building, we started changing. Playing the best on a yearly basis requires a level of preparation and you get used to it. The players love it.”
Nicolas Sanchez was Argentina’s heartbeat, interchanging with centre Juan Martin Hernandez at first receiver and playing flat to cause the Irish defence problems. He kicked 23 points and missed just one of his ten shots at goal, making Ireland pay for their indiscipline.
From a Sanchez bomb in the third minute, Tuculet leapt highest and set up a phase that ended with winger Santiago Cordero putting in Moroni for a try in the right corner. The second try came down the right, too, as Cordero ran into space and kicked on. Imhoff was the quickest of three Argentine chasers and managed to collect and ground before the dead-ball line.
When Sanchez booted a 14th-minute penalty for 17-0, the Irish needed to produce the greatest comeback in Rugby World Cup history.
A yellow card three minutes later to Argentina prop Ramiro Herrera for an illegal tackle gave Ireland hope, particularly when Robbie Henshaw’s pick-up-and-pass set free Luke Fitzgerald, on as an injury replacement for Tommy Bowe, to cut inside on the left wing and score a try converted for 20-10 at half-time.
Ireland began to challenge better at the breakdown and frustrate Argentina. And early in the second half, Fitzgerald provided more cutting edge by making a break through the middle and delivering a perfect offload that Jordi Murphy charged onto and over the line.
Sanchez and Ian Madigan booted penalties, and Ireland were only 23-20 behind with 20 minutes left. But Tuculet and Imhoff burst through a tiring defence to send the Irish home early again.
ARGENTINA: J Tuculet; S Cordero, Matias Moroni, Juan Martin Hernandez, Juan Imhoff; N Sanchez, M Landajo; M Ayerza, A Creevy, R Herrera, G Petti, T Lavanini, P Matera, J Fernandez Lobbe, L Senatore. Subs: J Montoya, L Noguera, J Pablo Orlandi, M Alemanno, F Isa, T Cubelli, J De La Fuente, L Gonzalez Amorosino.
IRELAND: R Kearney; T Bowe, K Earls, R Henshaw, D Kearney; I Madigan, C Murray; C Healy, R Best, M Ross; D Toner, IHenderson, J Murphy, C Henry, J Heaslip. Subs: R Strauss, J McGrath, N White, D Ryan, R Ruddock, E Reddan, P Jackson, L Fitzgerald.