The Pumas had the momentum in the first half and led 19-10 at half-time thanks to a lack of discipline from the visitors, who conceded nine penalties in the first 40 minutes.
But the Wallabies rallied and scored three tries in the second half to come home. Leading 27-26 in the 70th minute, the Wallabies boldly went to the corner again and Folau Fainga’a did what he does so often in Canberra and pounced. A try to Len Ikitau after the siren sealed the win.
Cooper appeared to tear a calf muscle in the 47th minute as he pushed off to try to start an attack. It seems likely that he will be exposed to a good part of the Rugby Championship, if not all of it.
Fraser McReight, who stepped in for Hooper, did his captain and the shirt proud with a busy performance that included a try.
Argentina led 19-10 after a first half often marked by the referee’s shrill whistle.
The Wallabies’ tendency against England last month to make life difficult for themselves in their own half continued from the start as two errors gave the Pumas the ball in the 22nd minute.
They escaped that time, but Pablo Matera didn’t take much longer to open the scoring when he took a nice inside ball from about 10 meters out and beat the covering defense of Allan Ala’alatoa to score the first points in the fifth minute.
The Wallabies responded with a penalty to Cooper from kick-off via strong defending, but they gave the three points back immediately by fouling from the restart.
Australia were unable to apply any serious pressure as they kept turning the ball over and when Adamson crashed down offsides the Wallabies were again pinged for another three points in the 15th minute.
The Pumas led 13-3, but they came back into the game with a bold decision to turn down easy points in the 16th minute. A lineout maul came to nothing, but Cooper did enough in the next phase to draw in two defenders and give Jordan Petaia an angled run to the line for a try.
But the penalties kept coming, Argentinian kicker Emiliano Boffelli knocking over another in the 20th minute.
Cooper had the chance to score a second try soon after when he made a clean break upfield but failed to pass to a flying Fraser McReight in support who would probably have scored. Another chance fizzled out soon after when James Slipper couldn’t hold a Cooper offload near the line.
A foul on Jed Holloway ended the half and Boffelli kicked another goal to extend the lead.
Holloway came close to scoring after Tom Wright had a good counter attack, but he had no support in the clearance and the ball was lost.
Cooper looked for another try in Pumas territory in the 47th minute when he slipped on some wet grass as he pushed off and he immediately hit the tire clutching his calf.
Players comforted him before he limped off, apparently aware it was a serious tear.
However, the Wallabies’ spirits quickly turned as they used a lineout maul near the line to score another try. McReight burst through the middle to finally chase down his first Test five-pointer.
The game and the scoreline tightened up, but the Pumas broke free again in the 55th minute when a sloppy kick chase allowed the hosts to break the line and an 80-metre move ended with Juan Martin Gonzalez scoring a well-taken try.
However, the game still had plenty of twists and turns to come. The Wallabies again entered Pumas territory and used the rolling maul and this time the referee pinged Argentina for illegally collapsing and awarded a penalty try.
A long-range penalty from Reece Hodge finally put the Wallabies ahead for the first time in the 64th minute.