But Gunaratne blasted three sixes and a four off Moises Henriques, meaning they needed 14 off the last over.
After Nuwan Kalesekara was dismissed off the first ball, Gunaratne belted a four and a six off Andrew Tye.
As was the case in game one, it came down to the last ball of the match, with Sri Lanka needing two to win.
Gunaratne smashed another boundary, sparking wild scenes of jubilation among the Sri Lankans as they reached 8-176.
He also top-scored with 52 in Friday night's win.
Earlier, Australia's under-strength attack had torn through the Sri Lankan top order as paceman Jhye Richardson impressed on debut and Andrew Tye was on a hat-trick.
But the first full international cricket match in Geelong attracted an underwhelming crowd of 13,537, with unseasonably poor weather undoubtedly hurting the attendance.
Richardson is one of Australian T20 debutants along with 36-year-old Michael Klinger, who followed up his 38 in game one with 43 on Sunday.
Henriques paced the Australian innings with an unbeaten 56, his first T20 international half century, while Kulasekara ended the innings with three wickets in four balls.
Gunaratne also took the key wicket of Ben Dunk, who had blasted 32 runs from 14 balls.
Australia made a surprise omission by leaving out legspinner Adam Zampa, who impressed on Friday night.
Australian captain Aaron Finch said Gunaratne's epic knock was one of the better T20 innings he had seen.
"That was definitely up there ... a guy who can hit it 360 (degrees) is such a dangerous player and so hard to defend (against)," he said.
"You have to have four fielders in the circle, so there's always somewhere exposed and if you have skills like that, it's hard to defend against."
Gunaratne, a quietly-spoken character, said with a smile it was the best he had batted."I was planning to finish the match at all costs and I was quite happy I could do that," he said through a translator.
"It certainly wasn't easy, but you had to come up with some plan and (tonight), it worked."
As Gunaratne spoke, several hundred Sri Lankan fans could be heard celebrating raucously outside the ground.
Several thousand expatriate fans have made the Sri Lankans feel like it was a home match.
"The fact we won the series was the greatest satisfaction ... it couldn't have been better," Gunaratne said.
"It was like playing at home away from home and the support (we've had) is a great strength."That made it a little easier."
