One of those wins was a shock bonus-point upset of world champions South Africa in Johannesburg, which came on the back of beating the British and Irish Lions as momentum builds under Joe Schmidt.
Every win is crucial at the moment for world rankings points before December’s draw for the 2027 World Cup, which Australia host.
The top-ranked nations, come December, will head each of the six groups, meaning they potentially avoid some of the big guns in the tournament pool stages.
Argentina are currently ranked seven to Australia’s six and the defeat will see them slide further behind.
The Pumas came into the clash full of confidence after their massive 29-23 takedown of New Zealand in Buenos Aires, but they faded badly in the second half.
Argentina struck first, with first five-eighths Carreras nailing a close-range penalty in the fifth minute, then he did the same from 40m several minutes later.
Wallabies prop Taniela Tupou was at fault both times for not using his arms in a tackle, earning an icy stare from Wilson.
Australia had more possession and territory but no points to show for it when they took a three-minute water break, because of the heat, midway through the half.
But they kept pressing and earned their reward when irrepressible halfback White nipped through a gap after a good carry from Wilson, with Tom Lynagh adding the extras.
The lead barely lasted with the Pumas stunning them with two free-flowing tries in four minutes.
Santiago Chocobares broke the defence out of a scrum and galloped clear before wing Delguy finished the move on the right, then Carreras dotted down after a break on the left.
Rubbing salt in the wounds, Carreras made one conversion then added another penalty to send them to the break on top.
Australia perked up after the break and quickly closed the gap to six points, with Suaalii surging through after an offload from Len Ikitau and Lynagh slotting the conversion.
With momentum on their side, Suaalii went over again from a set-piece and with James O’Connor adding the extras they were 21-21 with 17 minutes left.
Juan Cruz Mallia looked to have won it for Argentina when he kicked a penalty with two minutes on the clock, before the late drama and Bell’s try.