Scotland blew a 6-0 half-time lead as Argentina extended their 19-year winning streak at Murrayfield and inflicted Andy Robinson's first defeat in charge.
The home side put themselves on course to complete a clean sweep of autumn international victories for the first time since 2002 thanks to two Phil Godman penalties.
But Argentina turned the game on its head after the break, taking advantage of Nathan Hines' needless sin-binning with two penalties from Martin Rodriguez.
Rodriguez completed the comeback with a drop goal two minutes from time to hand the Pumas their fourth straight win in Edinburgh.
Robinson's 100% start as head coach had included beating Fiji and a historic win over Australia, while the Pumas had lost the opening two games of their UK tour against England and Wales.
But the visitors had also won seven of their previous eight encounters with Scotland.
After watching his side defend for almost the entire 80 minutes against the Wallabies, head
coach Robinson had demanded an improvement with the ball in hand.
He certainly got that in the first five minutes, two excellent periods of possession only let down by sloppy penalties.
But when Allan Jacobsen lashed out on halfway a minute later, Rodriguez had the chance to put Argentina ahead.
The centre made a hash of his penalty and Scotland eventually regained control.
And when Juan Martin Fernandez Lobbe was penalised for going over the top in the 14th minute, Godman kicked the home side ahead from 25 metres.
Scotland were matching Argentina's renowned ferocity up front, while centre Ben Cairns was justifying his recall with some elusive running.
His latest break earned Scotland a 19th-minute penalty, but Godman was well off target from near the touchline.
A minute later, a superb break by Sean Lamont should have led to a try but, despite getting within five metres, the home side could not breach the Pumas defence and Godman's
crossfield kick drifted into touch.
The build up saw Hines and Horacio Agulla embroiled in a wrestling match away from the main action, but both escaped punishment.
Argentina should have been made to pay for more ill discipline in the 24th minute but Godman missed a very kickable 35-metre penalty. The game was becoming a gruelling forward battle but a brilliant kick and chase from Rory Lamont broke the monotony four minutes from the interval, leading to a penalty Godman converted from almost 40 metres.
Despite bungling their kick off, Argentina began the second half as brightly as Scotland had started the first.
Chris Cusiter was forced to touch down behind his own tryline to prevent the Pumas scoring, with Rory Lamont appearing to hurt his left leg badly in a tackle.
While the full-back was receiving treatment, a wound-up Hines was sin-binned for a spear tackle on Gonzalo Tiesi.
