And it was Folau, who shot to fame with two tries during the first Test against the British & Irish Lions this summer, who provided the key intervention for the hosts in Perth.
The NSW Waratah wriggled his way through three would-be tacklers to go over in the right corner for the decisive score just before the half-hour mark.
Before that it was the visiting Pumas that had taken the lead as Nicholas Sanchez slotted a penalty from right in front.
But Christian Leali'ifano successfully kicked two penalties of his own in response for McKenzie's side before Folau had his moment.
Nic White, starting at scrum-half in place of the dropped Will Genia, produced quick ball over several phases as the Wallabies poured towards the line.
But it took a bit of magic from league convert Folau to finally unlock the stubborn Pumas, the full-back cutting back on the angle and powering his way past three Pumas to dive over.
Leali'ifano's conversion attempt was narrowly off target but he made up for that with a penalty on the stroke of half-time that put the hosts into a 14-3 lead.
The weather worsened in the second half and it was the visiting Pumas who grew into the encounter.
Sanchez's second penalty reduced their arrears but there was better still to come for the away side.
As the forwards drove them deep into the Australian 22 it was the wily Felipe Contepomi who unlocked the defence, breaking a tackle and off-loading superbly to Juan Manuel Leguizamon who barrelled over from close range after 65 minutes.
Leali'ifano was then a long way off target with a relatively simple penalty and with ten minutes to go it was still only a point that separated the two sides
But Australia did well to strangle the life out of the game as Argentina faield to get out of their half and coughed up possession with a couple of mistakes as they chased the game.
Leali'ifano was again off target with a long-range penalty with two minutes to go but the visitors could not muster a final response and the McKenzie's side held on for their first win since beating the Lions in the second Test in Melbourne.