The chase was far from comfortable, with India requiring 39 runs from the final three overs.
Kohli reduced that equation to 20 off the final two after belting James Faulkner all over the park.
The gifted batsman attacked Nathan Coulter-Nile with similar success, finishing 82 not out as the tournament favourites hauled in the target with five balls remaining.
"This innings has to be in my top three, perhaps the top right now because I'm a bit emotional," Kohli said.
Shane Watson starred in the topsy-turvy tussle, winding the clock back in his final game for Australia.
Watson removed Rohit Sharma and Suresh Raina in a haul of 2-23, while he claimed a scrambling one-handed catch to dismiss hobbled veteran Yuvraj Singh.
But Australia couldn't break the partnership that mattered most, with Kohli sinking to his knees after MS Dhoni struck the winning runs.
Kohli nailed the tricky run-chase as teammates succumb to fine bowling and immense pressure.
The 27-year-old seems to save his best for Australia and this dig was no exception, he rowed with Glenn Maxwell after taking exception with a return but never lost his cool.
Kohli picked gaps no matter what fields Smith set, turned ones into twos and stroked 11 boundaries in a marvellous man-of-the-match effort.
No shortage of questions will be asked in the postmortem after another failed shot at T20 glory from Australia, with shot selections and selectors' selections to be forensically analysed.
They were denied by a superstar who averages 122.83 in successful T20 chases for India but Smith will be stroppy his side failed to set a more imposing target.
Australia were unable to keep the scoreboard ticking over from overs five to 14.
Usman Khawaja and Aaron Finch blitzed the opening stanza, bringing up their 50-run partnership in just 3.4 overs after Smith won the toss and named an unchanged XI.
Momentum shifted dramatically after Khawaja was caught behind on 26, driving at a delivery from Ashish Nehra that nipped away from him.
David Warner, Smith and Finch, who top-scored with 43, all fell in a slump of 3-28 as India raced through their overs and dried up the boundaries.
After the opening four-over onslaught, Australia managed just 4-51 from their next 10 overs. It wasn't without controversy.
Smith was clearly furious and lingered at the crease after being judged caught behind on two by umpire Marais Erasmus.
Replays showed there was a gap between Smith's blade and Singh's first delivery of the tournament.
Watson and Peter Nevill hammered 15 runs off the final over of Australia's innings to give their side hope but Kohli was simply too good.
Match centre with scorecard, wagon wheel and Manhattan/Worm
