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Sri Lanka would have qualified for the WTC final if they had swept New Zealand in their two-match series and Australia denied India victory in the ongoing fourth test in Ahmedabad.
Kohli scored his first Test hundred since November, 2019. His 162-run stand for the sixth wicket with Patel was the highest in the Indian innings.
Opener Gill, playing his second match of the series, featured in three 50-plus partnerships to help India, who lead the series 2-1, reach 289/3 at stumps.
The Defenders will take on Bengaluru Torpedoes in the final on Sunday.
Cheteshwar Pujara top-scored for India with a gritty 59, while Nathan Lyon was the pick of the Australia bowlers, claiming 8/64.
The visitors, who are 2-0 behind in the four-Test series for the Border-Gavaskar Trophy, finished the frenetic opening day 47 runs ahead with six wickets in hand.
The Spikers won their first match of the season, 15-13, 14-15, 12-15, 15-7, 15-11.
Paceman Josh Hazlewood has already been ruled out with an Achilles injury.
The hosts finished a run behind Australia's 263 and the latter were 61/1 at stumps on day two.
India were 21 for no loss after bowling out Australia for 263.