Rinku, spinners help India down Australia to clinch T20 series
India posted 174-9 thanks to Rinku's 29-ball blitz, despite late strikes by the Australian fast bowlers after the tourists elected to field first in Raipur.
Axar then returned figures of 3-16 with his left-arm spin as the hosts kept down Australia to 154-7 to take an unassailable 3-1 lead in the five-match series.
"Other than (the) toss, everything went our way," India's Suryakumar Yadav said of the victory in his first series as captain.
"Winning was the big boost, especially the way the boys showed character. Everyone expressed themselves irrespective of the situation, and that's what I told them: be fearless, play your game and we'll see what happens."
Leg-spinner Ravi Bishnoi struck on his first delivery as he bowled Josh Philippe, for eight, and finished with figures of 1-17.
Axar struck in his first over to claim opener Travis Head's wicket, after his 16-ball 31 had given the tourists a quick start.
After derailing the opposition's chase, the Indian spinner kept up his strikes and sent Ben McDermott and Aaron Hardie back to the pavilion.
Tim David attempted to hit back but fast bowler Deepak Chahar took the batsman down, getting him caught in the deep on 19.
Chahar claimed another victim in Matthew Short on 22 as the wheels came off the chase, before skipper Matthew Wade hit a valiant 36 not out.
"We want to continue to learn about the players under the established players since the (T20) World Cup is around the corner, so depth around the squad will be key," said Wade.
Earlier, the left-handed Rinku put on key partnerships including a 56-run fifth-wicket stand with Jitesh Sharma, who hit a 19-ball 35.
Ben Dwarshuis took two wickets in the 19th over and fellow left-arm quick Jason Behrendorff also struck twice in the next over to deny Rinku his fifty and check India's surge.
Hardie began with a maiden over and in his second over cut short Yashasvi Jaiswal's brisk knock of 37 off 28 balls, after the left-hander mistimed a pull to get caught at mid-on.
Leg-spinner Tanveer Sangha sent back Shreyas Iyer for eight and Dwarshuis made the hosts slip to 63-3 when he got Suryakumar caught behind for one.
Ruturaj Gaikwad, who made 32 after his unbeaten 123 in the previous match, and Rinku put on a quick 48-run stand, which was eventually broken by Sangha.
Australia were without their ODI World Cup stars, including Glenn Maxwell, who hit a match-winning 104 not out in match three, and Marcus Stoinis.
Head remains the only player from the World Cup-winning team in the Australian side.
The final T20 is on Sunday in Bengaluru.