Matt Banahan's late try failed to prevent England from succumbing to a Juan Martin Hernandez-inspired Argentina at the Estadio Padre Ernesto Martearena.
England appeared to be heading for a heavy defeat when they entered half-time 14-3 behind, but they ate into the Pumas' lead after the interval.
Andy Goode, who amassed a 17-point haul, slotted four penalties and a conversion of Banahan's expertly-taken 79th minute try only for Argentina to survive a tense climax and secure a 24-22 win.
Outfought and outwitted for much of the match, England paid the price for some feeble tackling that enabled the impressive Pumas to build momentum with the minimum of fuss.
Opposite Goode, Hernandez produced a masterclass, mixing up attacking kicks with some clever off-loading and incisive running.
The imperious Stade Francais fly-half kicked three penalties, a conversion and drop goal to keep Argentina in control for most of the match with Juan Manuel Leguizamon and Gonzalo Camacho running in tries.
England often failed to match the Pumas' intensity at the breakdown and tackle area but showed real spirit to reel in their opponents when at one point they seemed to be chasing a lost cause.
England's preparations for the Autumn International series were potentially dealt a further blow as Maro Itoje was forced to undergo an x-ray after Saracens' European victory over Scarlets on Saturday night.