Steve Smith hammered 105 off 93 balls and Aaron Finch returned to form with 81 as Australia scored 328 for seven after electing to bat in the World Cup semi-final against India in Sydney on Thursday.
The pair shared a second-wicket stand of 182 before the defending champions hit back with quick wickets as the hosts stumbled from 191 for one in the 35th over to 248 for five in the 43rd.
But Shane Watson (28), James Faulkner (21 off 12 balls) and Mitchell Johnson (27 not out off nine) boosted the total to leave India facing a stiff target of 6.7 runs an over to qualify for Sunday's final against New Zealand in Melbourne.
It was the first time the 300-run mark was crossed in a World Cup semi-final, but teams batting second have won nine of the last 12 one-day internationals at the Sydney Cricket ground.
Off-spinner Ravichandran Ashwin finished with an impressive one for 42 from 10 overs, but in-form seamer Mohammad Shami went for 68 runs in 10 wicketless overs.
A sell-out crowd of some 42,000 at the SCG were treated to enthralling cricket on a grassless, even-paced wicket that enabled batsmen to play shots freely.
India removed David Warner in the fourth over as the left-hander, who had smashed a six over mid-wicket in Umesh Yadav's previous over, miscued a similar pull shot and was caught in the covers.
The Australians, given a lesson on how to play the turning ball by spin legend Shane Warne at the nets on Wednesday, prospered as Finch and Smith settled down to hammer the Indian bowling.
Indian captain Mahendra Singh Dhoni reluctantly asked for a television review when umpire Richard Kettleborough turned down an appeal for leg-before against Finch, on 43, off left-arm spinner Ravindra Jadeja.
Third umpire Marais Erasmus agreed with his colleague and Finch, whose top score after making a century in the opening match against England was 24, brought up his half-century in the 27th over.
Smith reached his fourth one-day hundred in the 33rd over, pulling seamer Mohammad Shami for his 10th boundary after hitting a six and four earlier in the over.
India separated the pair in the 35th over when Smith hooked a short ball from Yadav to Rohit Sharma on the square-leg fence.
Smith's wicket came during the batting powerplay taken by the Australians in the 33rd over, the five-over bracket producing 64 runs.
Glenn Maxwell smashed three fours and a six in a 14-ball 23 before he swept Ashwin to Ajinkya Rahane on the backward square-leg fence.
Finch fell one run later, caught by a leaping Shikhar Dhawan at short mid-wicket off Yadav, as the hosts slipped from their comfortable position to 233 for four in the 39th over.
Skipper Michael Clarke made a scratchy 10 when he was dismissed by Mohit Sharma to a catch at mid-wicket to reduce Australia to 248 for five.
Australia scored 57 runs in the last five overs to ensure they surpassed the 300-run target.
Both teams retained the same sides that won quarter-final matches, Australia beating Pakistan by six wickets in Adelaide and India going past Bangladesh by 109 runs in Melbourne.
Source: AFP
