At the toss, skipper Hardik Pandya said Arshdeep Singh was not available for selection.
With India's win, the five-match series is levelled 1-1.
Australia, with this win, took a 1-0 lead in the five-match series.
Another 12,000 tickets were made available for the public through the district associations, and those were sold over the counters.
Bumrah was on Thursday ruled out of the upcoming T20 World Cup due to a back stress fracture.
Arshdeep Singh was the pick of the Indian bowlers with figures of 3/32, while Deepak Chahar and Harshal Patel grabbed two wickets each.
Jasprit Bumrah complained of back pain during India's practice session on Tuesday. The BCCI Medical Team assessed him and he was then ruled out of the first game.
The match was reduced to an 8 overs-a-side contest after overnight rain left the outfield wet.
"I think we were 20 runs short. Credit to our bowlers for keeping us in the game," India captain Harmanpreet Kaur said after the game.
"We do have plans for all batters, but it was important that we executed them, the fielders supported the bowlers well," Harmanpreet said after the match on Tuesday night.
The 35-year-old talismanic batter achieved the milestone on Wednesday en route his 31-ball 40.
India once again showed a start-to-finish aggressive intent while reaching 170 for eight riding on new 'batting all-rounder' Ravindra Jadeja after a sudden collapse during the middle-phase.
The swashbuckling all-rounder became only the fourth player from full member nations to score a fifty and take four wickets in a T20I match.
Call it strangely pleasant, but it remains a fact that in this series a lot of things haven't exactly gone as per plan but yet India have managed to level the series after being 0-2 down.
Cricket Ireland has confirmed that the Indian team would be touring Ireland for a short two-match T20I series in June.
Mike Hesson acknowledged his England counterpart's concerns about burnout among players and staff but said T20 had an important role to play internationally.
India have so far lost all their matches against New Zealand, the fifth and last one coming at the ICC World T20 in 2016.