Australia will need to produce a record-breaking sub-continental run chase for an unlikely victory on the final day of the third Test against Sri Lanka in Colombo.

Sri Lanka set an imposing victory target of 324 runs after Angelo Mathews declared at 8-347 in their second innings early on Wednesday after resuming on 8-312.

Dhananjaya de Silva finished on 65 not out to go with his match-turning 129 in the first innings while Suranga Lakmal was unbeaten on four.

The only time Australia have successfully chased 200 or more in Asia was against Bangladesh in 2006 when they made 7-307 in the first Test in Fatullah.

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Australia will have a minimum of 83 overs to reel in the target.

One of David Warner, Shaun Marsh or Steve Smith will likely need to make a quickfire century to give Australia any kind of hope while the forecast of early afternoon rain might also play a part.

A Sri Lankan win would seal a 3-0 series whitewash and also Australia's ninth straight defeat in Asia following a 2-0 loss to Pakistan in the UAE in 2014 and 4-0 hammering in 2013 at the hands of India.

The way Australia have batted this series, Sri Lanka have plenty of runs to play with and can attack with their three spinners - Rangana Herath, Dilruwan Perera and Lakshan Sandakan - from the start.

They will be itching to have a crack on the parched pitch that has been baking under the hot Colombo sun.

Sri Lanka made 268 in the fourth innings a year ago but still lost chasing 386 against India.

There were some big last-innings totals made in 2009 but that was before the square was re-laid.

Nathan Lyon (4-123) and Mitchell Starc (2-72) were best with the ball for Australia.

Starc was clearly frustrated early on the fifth day with the foot holes and he delivered a wicked beam ball to de Silva that also beat wicketkeeper Peter Nevill.

The five no-balls in some way summed up Australia's arduous tour.

AUSTRALIA'S HIGHEST SUCCESSFUL TEST RUN CHASES IN ASIA:
- 7-307 v Bangladesh in Fatullah, 2006
- 2-195 v India in Bangalore, 1998
- 3-123 v Pakistan in Lahore, 1959
- 2-112 v Pakistan in Dhaka, 1959
- 2-67 v India in Mumbai, 1969

- AAP