Including that six sent over Starc's head, Allen took 14 runs from the opening over. The next, he cracked Josh Hazlewood to the boundary through the covers, and in the third over he pulled Pat Cummins over the square-leg fence.
In the space of 15 minutes, Australia's renowned pace attack had been blitzed. Although Allen fell to Hazlewood in the fifth over, his 16-ball knock of 42 put the Black Caps in a position of dominance they would never cede.
Devon Conway, who saw closely how cleanly the ball was being struck, credited Allen for laying the platform for his own outstanding innings of 92 not out, the pair having formed a stand in line with their ideal plan.
"We always say we want to start well and put teams under pressure, and the way Finn Allen batted up front was pretty special," Conway said. "They are a classy bowling attack, the three of them together. I have to give a lot of credit to Finn and the way he played.
"The way he put them under pressure allowed me to get those balls that were slightly looser. In T20 cricket, if you put bowlers under pressure, no matter how good you are, it's quite a tough gig.
"A lot of credit has to go to Finn for the way he played from ball one. He hit ball two for a boundary and we were away."
The Black Caps ended on 200-3, the highest total Australia had conceded at a T20 World Cup. Tim Southee then picked up 3-6 in a bowling attack that snagged regular wickets, while Glenn Phillips sparked a flawless fielding display with a flying grab to remove Marcus Stoinis.
The 89-run victory and the boost in net run rate it brought left New Zealand already in a strong position to reach the semifinals, with their next match coming against Afghanistan on Wednesday.
It also broke an 11-year drought without a win against Australia in their own conditions. But having often opened together in rather less illustrious circumstances for Wellington, Conway said he and Allen were never fazed by the occasion.
"I think it's irrelevant for us. We're just playing another game of cricket and it happens to be at the SCG against Australia.
"We just try and keep it the exact same. I know he's a very clean striker of the ball and I'm sort of that player who likes to bat around him and try to get him on strike as much as possible."