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Australia 225 for 5 (Maxwell 104*, Head 35, Bishnoi 2-32) beat India 222 for 3 (Gaikwad 123*, Suryakumar 39, Tilak 31) by five wickets
Guwahati: Glenn Maxwell hit the joint-fastest T20 century for Australia as the tourists kept alive their series hopes against India in Guwahati.
Maxwell smashed an unbeaten 104 not out from 48 balls, in a knock which contained eight fours and eight sixes.
Ruturaj Gaikwad's equally brilliant 123 not out from 57 balls helped set Australia a target of 223, which they reached off the final ball.
India now lead the series 2-1 with two matches to play.
Australia knew they had to win the third T20 of the five-match series to stand any chance of winning the series.
India started slowly and were 81-3 in the 11th over, when captain Suryakumar Yadav came in to partner Gaikwad.
Their explosive partnership put on 141 runs, with Gaikwad becoming the first India player to score a T20 century against Australia.
In response, Australia fell from 66-1 to 134-5.
Maxwell, however, went on to make history with his century. He reached three figures off 47 balls, the joint-quickest by an Australian in T20 history, emulating Aaron Finch and Josh Inglis.
In what was a remarkable final over, and one that bowler Prasidh Krishna would want to forget, Maxwell struck a six from the third delivery and followed it with three fours to snatch victory.
The fourth T20 takes place in Raipur on Friday, with the series concluding on Sunday in Bengaluru.
Both sides are set to have less experienced squads for the rest of the series.
Suryakumar was the only India player to have featured in the World Cup final defeat against Australia nine days ago that played in the third T20.
For Australia, World Cup winners Maxwell, Inglis, Marcus Stoinis, Steve Smith, Adam Zampa and Sean Abbott will all return home, leaving Head as the only World Cup winner still in India.
Wicketkeepers Josh Philippe and Ben McDermott, left-arm pace bowler Ben Dwarshuis and off-spinner Chris Green will all link up with the squad for the remainder of the tour.
