New ball bowler Bollinger dismissed Sachin Tendulkar (10) and Yuvraj Singh (6) off successive overs in his opening spell before claiming Mahendra Dhoni (24), Harbhajan Singh (zero) and Ravindra Jadeja for 57 to bowl out India for 170.
All-rounders Jadeja and Praveen Kumar (54 not out) struck fifties and shared in a 74-run stand for the eighth wicket to lift the hosts, who were tottering at 27 for five after choosing to bat first on a two-paced pitch.
In-form Shane Watson struck 49 but the world champions suffered a mini collapse when off-spinner Harbhajan Singh took the wickets of Watson and Ricky Ponting (25) in quick succession.
Michael Hussey (35 not out) put on 53 for the fourth wicket with Cameron White (25) and 29 with Adam Voges (23 not out) to guide the team to victory in 41.5 overs.
The last match will be played in Mumbai on Wednesday.
Scoreboard from the sixth limited-overs international
Virender Sehwag b Johnson 6
Sachin Tendulkar c and b Bollinger 10
Gautam Gambhir b Johnson 0
Yuvraj Singh b Bollinger 6
MS Dhoni lbw b Bollinger 24
Suresh Raina c Hauritz b Johnson 0
Ravindra Jadeja c White b Bollinger 57
Harbhajan Singh b Bollinger 0
Praveen Kumar not out 54
Ashish Nehra b Watson 4
Munaf Patel b Watson 0
Extras: (1b, 1lb, 3nb, 4w) 9
TOTAL: (all out) 170.
Overs: 48.
Fall of wickets: 1-7, 2-7, 3-23, 4-24, 5-27, 6-75, 7-75, 8-149, 9-170, 10-170.
Bowling: Mitchell Johnson 9-1-39-3 (4w), Doug Bollinger 10-4-35-5 (3nb), Clint McKay 10-1-44-0, Nathan Hauritz 9-2-19-0, Shane Watson 8-0-27-2, Adam Voges 2-0-4-0.
Shane Watson c Sehwag b Harbhajan Singh 49
Shaun Marsh lbw b Patel 6
Ricky Ponting c Raina b Harbhajan Singh 25
Cameron White lbw b Raina 25
Michael Hussey not out 35
Adam Voges not out 23
Extras: ( 6b, 2lb, 1w) 9
TOTAL: (for 4 wickets) 172.
Overs: 41.5.
Fall of wickets: 1-24, 2-85, 3-90, 4-143.
Did not bat: Graham Manou, Mitchell Johnson, Nathan Hauritz, Doug Bollinger, Clint McKay.
Bowling: Praveen Kumar 2-0-10-0, Ashish Nehra 3-0-21-0 (1w), Munaf Patel 4-1-13-1, Ravindra Jadeja 10-1-36-0, Harbhajan Singh 10-1-23-2, Yuvraj Singh 7-1-29-0, Suresh Raina 3-0-13-1, Virender Sehwag 2-0-8-0, Sachin Tendulkar 0.5-0-11-0.
Toss: Won by India.
Umpires: Asoka de Silva, Sri Lanka, and S.K. Tarapore, India.
TV Umpire: Sanjay Hazare, India. Match Referee: Chris Broad, England.
Result: Australia wins by 4 wickets.
Series: Australia leads 4-2 in seven-match series.