The hosts had set the tourists 299 to win, with Shaun Marsh scoring 131 off 123 balls.

Kohli was the foundation of India's response but holed out to Glenn Maxwell off Jhye Richardson to leave his side needing 57 runs off the final 38 balls.

MS Dhoni (55) and Dinesh Karthik (25), both unbeaten, saw the tourists home.

The deciding match of the series will take place on Friday in Melbourne.

Australia's Marsh hit 11 fours and three sixes on his way to a seventh ODI century.

But the home side were left to rue not setting a higher total after Indian bowlers Bhuvneshwar Kumar and Mohammed Shami took a combined 4-17 in the last 18 balls.

India paced their reply with Kohli at the helm and, despite his dismissal, Dhoni took over to complete the win.

Dhoni, playing in his 334th ODI, was struggling in the Adelaide heat late on but scored an unbeaten 55 from 54 balls, which included two sixes as his only boundaries.

"Tonight was an MS classic," Kohli said. "He takes the game till the end, when only he knows what's going on in his mind, and he backs himself to hit those big shots at the end.

"And hats off to Dinesh too, he came in and took the pressure off him."