Stanlake, making his first global appearance for a year, took wickets with his first two balls and removed Tom Bruce in his second over as the Black Caps could only muster 117-9 at the SCG.
Lynn (44 off 33 balls) and Maxwell (40 not out off 24 balls) shared a scorching 77-run stand from just 53 balls to steer Australia to the rain-reduced total of 95 from 15 overs with 21 balls to spare.
"It's great for him to hit the ground running, because he's a guy who can get nervous early on so it was great for him to get early wickets". Not only did he constantly clock over 150 kmph, but also snapped the New Zealand openers - Martin Guptill and Colin Munro - off his first two deliveries, and laid the platform of the visitors' collapse.
"He's getting quicker, he's getting taller and he's swinging the ball", said Lynn.
"We probably didn't assess conditions well enough, Australia bowled very well and there was a little in the wicket but we weren't able to soak that up", Taylor said.
"The first over seemed to settle me down a bit so that was nice".
Andrew Tye claimed four wickets as Australia restricted New Zealand to a below-par 117 for nine off 20 overs.
They also helped to limit Black Caps captain Kane Williamson to the slowest innings of his 47-match global T20 career, before Andrew Tye had him caught off a leading edge at cover for eight off 20 balls.
Tye mopped up the Kiwi tail to finish with four wickets for 23.
Only Colin de Grandhomme provided any real counterattack for New Zealand, with his unbeaten 38 from 24 balls featuring three massive sixes square off Tye and Adam Zampa.
Black Caps batsman Ross Taylor has praised teammate Colin de Grandhomme, after the all-rounder played the lone hand in New Zealand's seven-wicket loss to Australia in Sydney last night.