On Wednesday, Kohli was supported well by Suresh Raina (71 not out) and Yuvraj Singh (58) as the home side reached its target of 290 in 48.5 overs.
For Australia, Captain Michael Clarke made an unbeaten 111. He was associated in two big stands with Michael Hussey (69) and Cameron White (89 not out) that lifted the team to 289-3 after they were 16-2 in the eighth over.
The first match at Kochi was washed out while the third and final match will be at Margao in Goa on Sunday. Australia lost the two-test series 2-0.