Australia require seven wickets and Sri Lanka 260 runs for a history-making win on what promises to be a compelling final day of the second cricket Test at Bellerive Oval here on Tuesday.
The match, so much under Australia's control, can be snatched away by the Sri Lankans, but they will have to defy history to achieve their come-from-behind win after a heavy defeat in the first Test.
Australia set Sri Lanka 507 runs to win in five sessions. Only three teams in Test cricket history have scored beyond 400 runs for a fourth innings victory.
It looked as though Brett Lee had undermined Sri Lanka's hopes with two crucial wickets late on Monday's fourth day.
The pace spearhead lured Marvan Atapattu into a trap for his favoured hook shot and then bowled first-innings centurion Mahela Jayawardene next ball to put the Australians in the box seat.
But a fluent century from Kumar Sangakkara, his 15th Test hundred, late in the day gave the Sri Lankans some hope of pulling off a stunning victory.
The Australians are closing in on their 14th consecutive Test victory and are looking for another convincing win to wrap up the series 2-0 after an innings and 40-run win in Brisbane.
"Hopefully, we can start tomorrow very well," Australian skipper Ricky Ponting said. "We've got the new ball only 10 overs away. It would be nice to get a wicket early with the old ball and then expose a new batsman to the new ball.
"If we're not good enough to win the game with 500 on the board and five sessions up our sleeve, then it wouldn't matter how long we had."
At the close, Sangakkara was unbeaten on 109 in 292 minutes with Sanath Jayasuriya not out 33 in an unbroken 89-run stand. Sri Lanka were 247 for three.
"You've got to be realistic, 507 is a massive ask but the direction in which we go to tomorrow is now basically up to us," Sangakkara said.
"If we can get through to lunch without losing a wicket and depending on the amount of runs we get then things will get a lot clearer. We always go into the middle with a lot of belief."
Lee, Australia's outstanding bowler of the two-match series with 14 wickets, broke Atapattu's stubborn 143-run second-wicket partnership with Sangakkara.
He set up Atapattu on 80 for the hook shot and the batsman hit the ball straight to the safe hands of Phil Jaques, positioned on the square leg boundary.
Lee galloped down the pitch in elation when he bowled Jayawardene with his next ball with a reverse swinging delivery that collected off-stump and left the Sri Lankan skipper shaking his head in disbelief. Jayasuriya saw off Lee's hat trick ball.
Atapattu, 36, probably playing in his last Test for Sri Lanka after seeking a playing stint with a Sydney club, defied the Australian attack for 215 minutes, hitting nine fours off 164 balls.
His partnership with Sangakkara had stabilised the innings on a benign pitch after opening partner Michael Vandort made a hash of a pull shot and dollied an easy catch for four before lunch.
Sangakkara, who missed the Brisbane Test loss with a hamstring injury, reached his elegant century with a boundary off a full toss from out-of-sorts leg-spinner Stuart MacGill.
Lee's dismissal of Jayawardene was a huge one for Australia after the Sri Lankan skipper topscored with 104 in the first innings.
Ponting, who remained unbeaten on 53 with Mike Hussey on 34, made the declaration 45 minutes before lunch, giving his bowlers just over five sessions to bowl out the Sri Lankans.
The Sri Lankans will have to create history to win the Hobart Test.
Opener Phil Jaques was the only Australian wicket to fall on Monday, caught on the point boundary by Vandort off Lasith Malinga for 68.