Australia have defeated Sri Lanka by 137 runs to win the first Test match in Hobart.

The match looked to be heading for a draw after Sri Lanka reached tea on 186-4, but six wickets in the final session saw Australia bowl out Sri Lanka for 255 to secure a thrilling victory.

Resuming day five on 65-2, Kumar Sangakkara and Mahela Jayawardene got their side off to a solid start in taking Sri Lanka into three figures.

However, Jayawardene soon fell for 19 runs, edging the ball to Michael Clarke off the bowling of Peter Siddle.

Sri Lanka reached lunch on 144-3 but soon after the restart, they were dealt a huge blow when Sangakkara walked for 63 after being trapped lbw by Siddle.

Thilan Samaraweera was batting nicely and looked to be edging towards his half-century as he took Sri Lanka past 200, but Sri Lanka lost their fifth wicket when Angelo Mathews edged to Matthew Wade for 19.

That put the onus on Samaraweera to bat to the close but he fell just one short of a 31st Test 50 when Siddle trapped him lbw for his fourth wicket.

Sri Lanka were reeling and Mitchell Starc struck twice in quick succession to leave the tourists on 247-8 with 17 overs still remaining in the day.

Australia surrounded the bat and their pressure paid dividends as Rangana Herath deflected the ball onto his own stumps as Starc joined Siddle in picking up a four-wicket haul.

Shortly after, Starc secured his fifth wicket to hand his side victory when Shaminda Eranga gloved the ball to Matthew Wade.