Haddin slammed six fours and a six in his 62-ball innings before Yuvraj Singh struck in the 23rd over.
Haddin and Ponting held the fort in the middle, after losing Shane Watson, as they made steady progress in Motera as they took Australia past 100-run mark in good time.
Off-spinner R Ashwin provided India crucial breakthrough as he dismissed Australia's Shane Watson.
Openers Shane Watson and Brad Haddin started off well as they gave Australia a steady start against India. The duo added 40 runs for the first wicket.
Earlier, Australian skipper Ricky Ponting won the crucial toss and decided to bat first.
In what is Mahendra Singh Dhoni's 100th ODI as India captain, there is one change to the side with Virender Sehwag coming in for Yusuf Pathan.
Australia have brought David Hussey in place of spinner Steven Smith.
At the toss, Ponting said: "This pitch will slow up as the game goes on. 250 looks like a reasonable score. Our bowling against Pakistan was probably the best we did in the tournament."
Indian captain Dhoni said: "It will assist the spinners as the game goes on. Unless you don't think about pressure, there is no pressure. We are thinking about how we need to perform.
Teams:
India: Mahendra Singh Dhoni (c), Sachin Tendulkar, Virender Sehwag, Gautam Gambhir, Virat Kohli, Yuvraj Singh, Suresh Raina, R Ashwin, Harbhajan Singh, Zaheer Khan, Munaf Patel
Australia: Ricky Ponting (c), Brad Haddin, Shane Watson, Michael Clarke, Cameron White, Mike Hussey, David Hussey, Mitchell Johnson, Brett Lee, Jason Krejza, Shaun Tait.
Umpires: Marais Erasmus (RSA) and Ian Gould (ENG)
TV umpire: Richard Kettleborough (ENG)
Match referee: Ranjan Madugalle (SRI)
Pitch conditions: Usually proves an excellent batting surface so bowlers on both sides are set to have to be at their best to enjoy success.
