The Pumas had Marcos Kremer red-carded in the first half and then received three yellow cards after the break, leaving them with 12 men at one point, while Scotland also had two players sin-binned in the closing quarter.
Despite having at least a one-man advantage for almost three-quarters of the match, it was only in the closing stages that Scotland – inspired by the outstanding Finn Russell – were able to pull away and put the outcome beyond doubt.
The hosts got off to a bad start when they conceded a penalty within 20 seconds, after Jonny Gray entered the first ruck of the match illegally. Edinburgh wing Emiliano Boffelli duly put the first points on the board for Argentina when he sent his kick between the posts.
Scotland responded with a brilliant try in the 11th minute, when Sione Tuipulotu received a perfectly-timed offload from Russell and darted his way beyond a cluster of Pumas to score. Russell converted.
The home support were silenced five minutes later, however, when Jeronimo De La Fuente bounded over on the left despite the close attentions of Ali Price. Boffelli was wide with his conversion attempt.
Argentina’s hopes of a result were dealt a major blow in the 23rd minute when they were reduced to 14 men after back-rower Kremer was shown a red card for a dangerous tackle on Jamie Ritchie following a TMO review.
Scotland made the extra man count almost immediately as Russell offloaded to Duhan Van Der Merwe just in front of the line and the wing juggled the ball between his hands before forcing it down in the 25th minute. Russell was successful with the conversion.
Just three minutes later, the Scots scored again when Graham bolted his way over on the right after an excellent flowing move, with Russell the architect in chief – but this time Russell’s kick was inaccurate.
Argentina refused to capitulate and in the last action of the half, Matias Alemanno barged his way over to score following a sustained period of pressure in front of the Scottish line.
Boffelli converted to ensure the Scots went in only 19-15 ahead at the interval.
Scotland reasserted their authority just a minute into the second half, however, when Graham was released on the right following good play by Russell and Stuart Hogg. Russell hooked his kick wide of the posts.
Gregor Townsend’s side – at this point leading 24-15 – were presented with a great opportunity to turn the screw on their opponents going into the closing half-hour when the Pumas were temporarily reduced to 12 men after Alemanno and Tomas Lavanini were both sent to the sin-bin within a minute of each other.
Incredibly, despite having three men less than their hosts, Argentina scored a breakaway try when Boffelli raced beneath the posts in the 52nd minute and added the extras himself.
Three minutes later, Tuipulotu went over on the right for his second try of the afternoon, with Russell kicking the conversion.
Almost as soon as Argentina had welcomed their two players back from the sin-bin, a mass brawl erupted just after the hour mark which resulted in Scotland captain Ritchie and Pumas prop Thomas Gallo being yellow-carded.
The Scots eventually started to pull away from their bedraggled visitors in the closing 11 minutes when Cam Redpath, Hogg and Graham all helped themselves to tries, with Russell converting all three.
Tuipulotu was sin-binned right at the death, before Argentina replacement Ignacio Ruiz scored a try – converted by Nicolas Sanchez – in the last action of an eventful match featuring 12 tries and six cards.