Australia, set 222 for victory, lost half their wickets inside nine overs to be 72 for five.
Aaron Finch, their captain, kept them in the match with a fine innings of 84 while sharing a sixth-wicket stand of 86 with Ashton Agar.
But the run-rate required Finch to keep going for big hits and when he holed out off Adil Rashid, Australia were 158 for six in the 16th over.
Leg-spinner Rashid, the official man-of-the-match, led England’s attack with three for 27 in his maximum four overs before paceman Chris Jordan struck twice in two balls to leave Australia on the brink of defeat at 174 for eight.
Australia were bowled out for 193 with two balls to spare.
This latest reverse meant they had still to win an international match since Justin Langer became their coach after his fellow former Test batsman Darren Lehmann resigned in the fall-out from March’s ball-tampering scandal in Cape Town.
Buttler, fresh from his man of the series heroics in a 5-0 one-day international sweep of Australia, including a match-winning 110 not out in a dramatic one-wicket victory in the series finale at Old Trafford on Sunday, was promoted to open in this one-off T20 clash.
He responded with a 22-ball fifty, including six fours and four sixes, on his way to 61.
Alex Hales made 49 after Jason Roy (44) put on 95 for the first wicket with Buttler.
“Another fantastic performance,” England captain Eoin Morgan told Sky Sports.
“With the bat, we started off outstandingly well, with Jos up to the top of the order for us — he and Jason really did get us off to a flier, expressing themselves against that new ball.
“From there, we managed to kick on, didn’t take our foot off the pedal,” he added.
“With the likes of (Jonny) Bairstow coming in at No 6 and Moeen (Ali) at No 7, you can keep going hard. That really paid off today — we got about 15-20 over par and we needed them, with Australia coming back hard at us with the bat.”
Meanwhile, Finch said Australia’s top-order collapse left them in an awkward position.
“We thought if we could get the required rate down to about 13 or 14 an over, and with myself and Agar there at the end, we’d have half a chance, but then you’re only one mistake away from being down to the genuine bowlers.”
Buttler was soon into his stride after Finch won the toss and fielded, launching debutant leg-spinner Mitchell Swepson’s sixth ball for a straight six.
Roy should have been out for 27 when he drove left-arm spinner Ashton Agar straight to long-off only for Kane Richardson to drop a simple catch.
The next two balls saw Buttler scoop a four and smash a six.
An ‘inside-out’ six over extra cover off fast bowler Billy Stanlake was even more audacious.
The next ball saw Buttler go to fifty with a scooped four just beyond the reach of wicket-keeper Alex Carey.
Buttler eventually became Swepson’s first international wicket when he holed out in the deep, with Roy falling next over when he skied Stanlake to Finch at midwicket.
Hales kept the runs coming before he was brilliantly caught and bowled one-handed off Marcus Stoinis’s first ball after he flat-batted a bouncer.
Spin, Australia’s Achilles heel during the ODI series, then proved their undoing in this match.
After off-spinner Ali had Travis Head caught in the deep, Rashid took two wickets for no runs in three balls to leave Australia 72 for five.
First he bowled Carey (three) with a quicker delivery and then dismissed Stoinis for a duck when the all-rounder drove him straight to Roy at long-off.