"The intention was to put an impact on the game and probably provide a bit of energy for the boys, try and get a spark going."
Australian captain Aaron Finch won the toss and elected to field first in Perth, and immediately took a gamble by denying star paceman Mitchell Starc the new ball duties.
But the decision quickly paid dividends, with Pat Cummins removing Sri Lankan wicketkeeper Kusal Mendis in the second over of the match.
Pathum Nissanka and Dhananjaya de Silva combined for a 69-run partnership for the second wicket before Australian spinner Ashton Agar snared a crucial breakthrough in the 12th over.
Wickets started perpetually tumbling throughout Sri Lanka's innings, but the Asia Cup champions kept the scoreboard ticking by taking advantage of some sloppy Australian fielding, squeezing twos out of regulation singles.
Chamika Karunaratne and Charith Asalanka provided some late fireworks at the death, combining for an unbeaten 37-run partnership from 15 balls to steer Sri Lanka towards a defendable total of 6/157.
Starc was undeniably the pick of the Australian bowlers, finishing with 1/23 from his four overs, while David Warner was an absolute gun in the field.
Australia's run chase started poorly, with veteran opener Warner smacking Maheesh Theekshana's first delivery of the match towards the cover fielder.
Sri Lanka's pace bowlers unearthed plenty of seam movement during the Powerplay, getting the Kookaburra to jag viciously off the lively Perth deck.
For the first time in men's T20 internationals, Australia failed to score a boundary during the Powerplay.
West Australian all-rounder Mitchell Marsh finally found the middle of his bat before departing in the ninth over, removed by Sri Lankan spinner Dhananjaya de Silva for 18 (17).
Glenn Maxwell cracked four boundaries from his first six deliveries at the crease, quickly shifting momentum back in Australia's favour at the drinks break, but Sri Lanka refused to wave the white flag.
The visitors delivered 10 consecutive dot balls before removing Maxwell in the 13th over for 23, with substitute fielder Ashen Bandara taking a superb catch on the mid-wicket boundary rope.
Enter, Stoinis.
The West Australian repeatedly muscled Sri Lanka's spinners over the boundary rope, cracking four boundaries and six maximums to secure Australia's first victory of the tournament.
His wildly entertaining display of big-hitting was headlined by a 101m six off Sri Lankan spinner Wanindu Hasaranga in the 15th over.
Finch, who battled his way towards an unconvincing 31 not out (42), literally bowed down to Stoinis after the much-needed win.
Maxwell copped a terrible blow to the throat while facing Sri Lankan seamer Lahiru Kumara during the run chase, with the Victorian immediately whipping off his helmet and dropping to his knees after the 137km/h short ball struck his neck.
Thankfully, he was able to continue his innings.
Australia will next face England in a sudden-death blockbuster clash at the MCG on Friday evening.