Two tries in the space of four minutes in the third quarter proved decisive. Rafael Carballo finished with two touchdowns and Juan Martin Hernandez kicked 14 points after coming off the bench in the 32nd minute.
Referee Martin Fox decided the game could go ahead after an inspection 15 minutes before kick off and the Pumas included six capped players in the starting XV.
Northampton spent most of the opening 10 minutes battling to get out of their 22, but the Pumas could not find a way through despite a succession of penalties.
They ended up kicking at goal and Federico Serra screwed his attempt wide.
Fly-half Steve Myler - making his return after nearly two months on the sidelines with knee ligament damage - relieved the pressure and set up Northampton's first attack with a kick to touch inside the Pumas' 22.
But the pressure came to nothing and Serra missed a second penalty attempt for Argentina after 21 minutes.
Northampton drew first blood five minutes later with a penalty from France Under-21 international Matthieu Bourret, but the Pumas were soon level thanks to a Juan de la Cruz Fernandez Miranda drop goal.
Bourret missed a chance to put Northampton back in front after 34 minutes when his penalty attempt drifted wide.
Serra was more accurate in the 39th minute with a penalty that put the tourists 6-3 ahead and they went further clear in injury time through a couple of long-range penalties from replacement Hernandez.
Hernandez added another penalty within two minutes of the restart and another following an incident that led to Mark Hopley being sin-binned.
Northampton battled on in Hopley's absence but missed the chance to reduce the gap when Bourret sliced a penalty wide.
The home side regrouped and a catch and drive led to Damien Browne touching down for a try that Bourret converted to close the gap to 18-10 after 51 minutes.
The Pumas' response was immediate. Martin Gaitan carved through Northampton's defence and sent Serra over unchallenged in the corner.
Hernandez added the extras to make it 25-10 and Argentina soon went further clear.
Number eight Genaro Fessia picked up a loose pass from Northampton on the edge of his own 22 and charged forwards. The ball was switched out to the left wing and Carballo squeezed over in the corner.
Northampton refused to throw in the towel and Albacete's yellow card in the 67th minute was soon followed by the home side's first try from Hopley and Bourret's conversion made the gap 30-17.
Carballo bagged his second try in the 72nd minute after Northampton had been unable to deal with a Serra up-and-under, but Hernandez missed the conversion to leave the score 35-17.
Horacio Agulla completed the scoring with a last-minute try.