The Pumas scored four tries at Franklin's Gardens, with replacement Juan-Martin Fernandez claiming man-of-the-match honours after kicking 17 points.
A crowd of 8,592 braved the cold to watch the game and, after a couple of missed penalties by Argentina's Federico Serra, it was Saints who opened the scoring with a Matthieu Bourret penalty. But the visitors hit back with a Juan Fernandez Miranda drop goal to level the scores.
Serra then slotted his first penalty to give Argentina a lead they were not to relinquish for the rest of the evening.
Replacement full-back Fernandez then completed two penalties in first-half injury time - one from inside his own half - to give the Pumas a 12-3 lead and he stretched this to 15-3 before Damien Browne got the first try of the evening for Saints following a line-out.
But two quick-fire tries from Serra and Rafael Carballo, the former converted by Fernandez, made it 30-10 on the hour mark.
Saints did not give up, though, and No.8 Mark Hopley's converted try brought he gap down to 13 points before Carballo grabbed his second of the evening and Horacio Agulla touched down to complete the scoring.
The Pumas are now preparing for Sunday's PwC Challenge Cup match against Leicester Tigers at Welford Road.
Tickets are on sale now, with all junior tickets priced at just £5.
Contact the Tigers ticket office on 08701 28 34 30 or online at www.leicestertigers.com