Sri Lanka's new skipper Upul Tharanga won the toss and chose to bowl in the opening Twenty20 worldwide against Australia in Melbourne on Friday. Seamer Vikum Sanjaya was handed a debut.
With Sri Lanka seemingly cruising to victory needing 18 runs off the last three overs, Turner injected fresh excitement into the contest claiming two wickets in the 18th over.
That target was reduced to three from two balls amid increasing tension, but Chamara Kapugedera (10 not out) scrambled two from the penultimate delivery before cracking Tye through the covers for a boundary that sealed a five-wicket win and delighted a sizeable contingent of Sri Lanka fans.
Sri Lankan paceman Lasith Malinga made a successful return to worldwide T20s - he was on a hat trick late in the Australian innings, finishing with 2-29 from four overs, and also took two catches.
Dickwella and Munaweera fell in successive overs from Adam Zampa (2-26 from four), but the spinner was denied a third wicket when Australia captain Aaron Finch failed to take a hard chance leaping to his left at short midwicket, reprieving Gunaratne on 11.
The match was Malinga's first full worldwide in almost a year, because of injury and illness.
Australia: Aaron Finch (capt), Michael Klinger, Travis Head, Moises Henriques, Ashton Turner, Tim Paine, James Faulkner, Pat Cummins, Adam Zampa, Andrew Tye, Billy Stanlake.
Australia had several top players unavailable because of the India test tour.
Klinger, at 36 the oldest Australian T20 worldwide debutant, combined with Finch for a solid opening partnership of 76. "We probably lacked one or two 15-run overs, but there are many positives to take out of the game".
The teams now move to South Geelong, Victoria for the second Twenty20 match on Friday.