Reece Hodge missed a last-gasp penalty as 14-man Australia drew with the Pumas for the second straight game to confirm New Zealand as Tri Nations champions Saturday.
The Wallabies needed a crushing 101-point win over the Pumas, who were missing captain Pablo Matera and two others after lat week's racist tweet scandal, to overhaul the All Blacks in the tournament's final game.
Argentina needed to win by 93 points to lift the trophy, but a high-scoring match was never in prospect on a muggy night of steady rain in Sydney. Instead, they remarkably finished at 16-16, a fortnight after they couldn't be separated in a 15-all clash.
Hodge could have won the game but sent his 45-metre kick wide with a minute remaining, just as he did in the dying seconds of their drawn match two weeks ago.
Australia's discipline again let them down in the first half with Argentina going to the break 13-6 in front, scoring 10 points when Hooper was in the sin-bin for a high tackle. Lukhan Salakaia-Loto was then sent off with 20 minutes left but the Wallabies dug deep to save face.
The entertaining clash rounded out a southern hemisphere tournament reduced to three teams after World Cup holders South Africa pulled out over coronavirus issues.
The draw ensured Argentina finished second, capping a momentous tour by Mario Ledesma's men who endured lockdowns and a slew of Covid-19 cases before upsetting New Zealand then drawing with Australia a fortnight ago.
The Wallabies took the wooden spoon in a poor end to Rennie's first year in charge, which has seen them win just once.
It was battling effort by the Pumas, whose build-up was disrupted by the tweet scandal.
Matera, second row Guido Petti and replacement hooker Santiago Socino were all suspended after years-old "discriminatory and xenophobic" comments surfaced, before a shock U-turn saw them reinstated on Friday.
The posts emerged after criticism that the Pumas did not adequately pay tribute to late footballing icon Diego Maradona, who died last month, before last weekend's defeat by the All Blacks.
They all wore a No.10 on the sleeve of their jerseys on Saturday, in honour of Maradona, and were clearly fired-up.
"I think we deserved this one, I thought we could have won it," said Ledesma. "I'm really happy with the whole tour and couldn't be prouder of the guys... but this week has been hard, really tough especially on some of the boys and it was a really difficult week to prepare."
With playmaker James O'Connor back, the Wallabies enjoyed plenty of early possession and their pressure paid off when Pumas lock Marcos Kremer was yellow-carded on 15 minutes for a dangerous clean-out, with Hodge converting the resulting penalty.
But the lead lasted barely a minute with the golden boot of Argentina's Nicolas Sanchez levelling the score after a Matt Philip mistake from the restart.
Just as Kremer returned to the field, Hooper was sent to the bin for a similar offence after crunching Sanchez with a high shot.
It marked a momentum shift with the Pumas taking the lead when Domingo Miotti, on while Sanchez received attention, nailed a penalty after another Philip error.
Felipe Ezcurra then made a break from a maul and set free winger Bautista Delguy, who dived over for their first try in three Tests.
Miotti converted to put then 13-3 in front until another Hodge penalty on the half-time hooter clawed back three points.
Hodge booted another after the restart to reduce the gap but then Salakaia-Loto saw red for a dangerous tackle and it looked all over for the Wallabies.
But they refused to give up and Hooper barged over for a try from a line-out with Hodge converting to level the scores at 16-16.