New Zealand stun champions and hosts Australia in Super 12 opener
Expatriate New Zealanders turned out in numbers at a packed Sydney Cricket Ground and were treated to fireworks from the Black Caps batters as they blasted their way to 200 for three in their 20 overs after Conway smashed the final ball for a six.
Seamer Tim Southee struck early to remove David Warner and took three for six as the New Zealand bowlers kept up a relentless pressure to dismiss the hosts for 111 in the 18th over.
It was Australia's biggest loss in a T20 international and New Zealand's first win in any format against their neighbours in Australia since a test win in Hobart 11 years ago.
"It was an outstanding day," said captain Kane Williamson. "It was a very good total on that surface and I thought the bowling and fielding was outstanding.
"We know how good this Aussie side is but the boys showed a lot of ticker and took their catches. Yeah, it's a funny old game."
Finn Allen, one of four changes from the New Zealand team that lost last year's World Cup final to the Australians in Dubai by eight wickets, set the tone for the Group 2 match with a brutal 42 off 16 balls.
Dropped by Adam Zampa on 19, the 23-year-old opener pummelled five fours and three sixes before he was clean-bowled by a Josh Hazlewood yorker.
The pace dropped a little with Williamson at the crease but he still managed a respectable run-a-ball 23 before Jimmy Neesham (26 not out) came out to finish the innings with Conway, who hit his 92 off 58 balls.
Warner's unfortunate early departure for five - Southee's opening delivery came off his pad and bat and went back into his stumps - kept Australia on the back foot.
Mitchell Santner (3-31) took some early punishment but had Australia skipper Aaron Finch caught in the covers for 13 before Southee got his second wicket when Mitch Marsh was caught in the deep by Neesham for 16 before the end of the powerplay.
Marcus Stoinis departed for seven in the ninth over to give Santner his second victim but the honours for the wicket will go to Glenn Phillips, who raced around the outfield to take a diving catch for the ages.
Glenn Maxwell handed out some punishment with a 20-ball 28 but when he departed, the Australians were in all sorts of trouble at 89 for seven.
Trent Boult took two wickets to help mop up the tail but the final act of the match appropriately went to Conway, who took a comfortable catch behind the wickets after Pat Cummins had sent Southee's final delivery high into the night sky.
"They got the jump on us in the first four overs and we never really recovered from that," said Finch.
"We were just totally outplayed in all three facets."