Scotland played some of their best rugby of the tour but squandered a 15-point lead in the final 30 minutes to allow their hosts back into the game.
Emiliano Boffelli, the Argentine winger who plays his club rugby in Scotland, scored the decisive try in the final minute.
Scotland had lost the first match in Jujuy but after last weekend’s win in Salta, it looked as if Gregor Townsend’s side had turned things around.
Blair Kinghorn had his best game in the No 10 jersey at Test level and the Scots looked worth their lead which came courtesy of two tries apiece from Duhan van der Merwe and Ewan Ashman. But Argentina showed guts and made Scotland pay for their failure to manage the game in the final quarter.
Hamish Watson, captaining the national side for the first time, also cited problems at the set-piece.
“For parts of that game we dominated, we looked good,” said Watson, who took over the captaincy from the rested Grant Gilchrist. “But at the end of the day we were architects of our own downfall.
“We gifted them points. Credit to Argentina, they are a proud nation. Our setpiece wasn’t good enough either. If you can’t win your lineouts..."
Townsend is left with much to chew over with the Rugby World Cup less than 14 months away.
Boffelli squandered an early opening for Argentina when he dropped a high pass with the line at his mercy but the Edinburgh wing soon atoned. When the Pumas were awarded a penalty two metres inside their own half he had no hesitation in having a pop at goal and landed the three-pointer with a monster kick.
Scotland had been under the cosh in the opening ten minutes but they came out of their shell with an impressively improvised passing sequence which led to their first try. With Argentina scrambling to keep up, Kinghorn took the ball into contact and deftly offloaded to van der Merwe who powered his way over despite the efforts of the two Pumas defenders hanging off him. Kinghorn converted to give Scotland a 7-3 lead.
The stand-off had been instrumental in the score but he also had a hand - or more accurately, a foot - in Argentina’s opening try. Ali Price sought to open up the hosts with a chip over their backline and Kinghorn was first to it. The former Hearts youth player tried to dribble but the ball was collected by Bautista Delguy who launched an effective counter attack. Argentina took the ball up to the Scotland 22 and Boffelli played it inside to Carreras who ran in the score. Boffelli converted.
It had been a thrilling first 20 minutes and there was let up. The Scots were awarded a penalty on their opponents’ 22 and kicked for the corner rather than taking an easy three points. The gamble paid off as Ashman marked his first start for Scotland with a try from the subsequent lineout maul. Kinghorn’s conversion from wide on the left put Scotland 14-10 up but Boffelli reduced the lead with another penalty.
Perhaps inspired by his Edinburgh team-mate, Kinghorn decided to have a go with a long-range effort when Scotland were awarded a penalty a couple of yards inside their own half. Unfortunately for the stand-off, his fine effort struck the crossbar, but it had been an impressive first 40 for Kinghorn and he started the second half in similar fashion, playing in Ashman for his second try.
The hooker was lurking on the left flank when Kinghorn spun out his long pass and the finish was worthy of a winger. The conversion from close to the touchline was impressively executed once again by Kinghorn.
Scotland had their tails up and were putting together some quality phases. Mark Bennett, a try scorer in each of the first two Tests, ran an impressive line to take the visitors into the Argentina 22. They nibbled away, edging towards the line, with Hamish Watson and then Zander Fagerson going close before van der Merwe battered his way over from a yard out. Kinghorn’s conversion extended Scotland’s lead to 28-13 but the hosts were not about to chuck in the towel.
Argentina coach Michael Cheika had looked to his bench for inspiration and it two of his substitutes weighed in with a try apiece.
Nahuel Tetaz Chaparro got the first, the prop stretching out a hand to touch down after Argentina had made capital from the restart after van der Merwe’s try. Boffelli converted to reduce further Scotland’s lead but Kinghorn added a penalty to nudge the visitors 31-20 ahead after the Pumas were punished for a ruck transgression.
Things were starting to get tense and when Bertranou nicked Argentina’s third try it set up a grandstand finish. The sub scrum-half had scored against Scotland in the first Test and did it again in Santiago del Estero, picking up from the base of a ruck and diving at the feet of Bennett before the centre could react.
Boffelli’s conversion meant Scotland’s lead had been cut to four points with 12 minutes remaining.
The tourists were soon back on the offensive and were awarded a penalty inside the Argentina 22. Rather than take the three points, they kicked for the corner again but this time it backfired. They tried to catch the Pumas out with a disguised lineout move but Jonny Gray was held up and the chance was squandered.
Argentina smelled blood and they went for Scotland. Their forwards led the charge and they won a key scrum in the final minute close to the Scottish line. The ball was shipped out to the left wing and Boffelli cut back inside to score the winning try and clinch the series in the most dramatic fashion.
The Edinburgh back, who had been superb off the tee all night, had the final say by landing the conversion.
Scorers: Argentina: Tries: Carreras, Chaparro, Bertranou, Boffelli. Cons: Boffelli 4. Pens: Boffelli 2.
Scotland: Tries: van der Merwe 2, Ashman 2. Cons: Kinghorn 4. Pen: Kinghorn.
Argentina: J Cruz Mallia; B Delguy (L Cinti 49), M Orlando, M Moroni, E Boffelli; S Carreras, L Bazan Velez (G Bertranou 61); T Gallo (N Tetaz Chaparro 49), A Creevy (I Ruiz 58), J Sclavi (F Gomez Kodela 49), G Petti, T Lavanini (M Kremer 49), P Matera (c), S Grondona, F Isa.
Replacements: JM Gonzalez, T Albornoz.
Scotland: O Smith (R Thompson 74); R McLean, M Bennett, S Tuipulotu, D van der Merwe; B Kinghorn, A Price; R Sutherland ( P Schoeman 52), E Ashman (D Cherry 52), Z Fagerson, S Cummings (G Young 69), J Gray, R Darge, H Watson (A Christie 74), M Fagerson.
Replacements: J Sebastian, G Horne, S Johnson.
Referee: Ben O’Keeffe (New Zealand).