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.
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.
They endured a miserable start at the line-out with Dylan Hartley wayward on two throws - the second of which was punished with a Pumas try after just two minutes.
Marion Ledesma, who had already made a wrecking-ball run, came up with the ball at the foot of the set-piece before feeding the onrushing Leguizamon and the Stade Francais number eight charged over.
It was an ominous start by Argentina but England recovered well with Andy Goode striking a penalty and then producing a massive touch finder to sweep his side out of the 22.
Ill-discipline began to creep into England's game as Argentina's pressure took its toll, conceding two penalties that Hernandez slotted over.
In contrast to Old Trafford, the Stade Francis had options outside him with centres Santiago Fernandez and Gonzalo Tiesi and full-back Horacio Agulla running off his shoulder at pace.
England were clinging on, their flimsy tackling enabling Argentina to build easy momentum while the Pumas approached their defence work with far more vigour.
Chris Robshaw was smashed backwards and Argentina won the ball, giving the imperious Hernandez another chance to run rings around the visitors' defence.
A crafty chip by Goode gave England a sniff of the line but the space was closed quickly and a long pass to an unmarked Banahan went forward.
The second half was just three minutes old when Argentina ran in their second try, courtesy of a missed tackle by Goode.
Agulla came charging into the line, swatted aside Goode and sent out a superb long pass to winger Gonzalo Camacho who dashed home unopposed.
Hernandez landed the conversion but England struck back with their most promising passage of play as Goode began to run the ball.
Struggling to contain the assault, Argentina conceded three penalties which Goode sent over and then had Agulla to thank for coming to the rescue as May threatened to gather a chip over the top.
The Pumas took their foot off the pedal in the final quarter amid turnovers from both sides.
Goode booted his fifth penalty to take England within a converted try of victory but with impeccable timing Hernandez booted a drop goal.
England were not finished, however, as they produced a fine move to set up a grand stand finish with four minutes to go.
Delon Armitage, who had been solid all match, broke free down the left wing and slipped a superb pass to Banahan who bounced off Francisco Leonelli to cross under the posts.
Goode converted but England could not get their hands on the ball again and Argentina held out for victory.
