Australia, playing their first full ODI following their long break after claiming a World Cup hat-trick in April, overcame early trouble to amass 306 for six on being asked to bat first.
India, on a high since winning the Twenty20 title, were all out for 222, conceding a 1-0 lead in the seven-match series which began with a rain-abandoned fixture.
Symonds shared 108 runs for the fifth wicket with Haddin, who was unbeaten after his second successive fifty, after adding 94 runs with opener Matthew Hayden (75) for the fourth wicket to rescue the innings from two for eight runs in the fourth over.
Haddin was named Man of the Match.
Fast bowler Stuart Clark removed Sachin Tendulkar (16) in his first over and trapped the aggressive Robin Uthappa (41) in reply to reduce India to 87 for four and snuff out the chase.
Skipper Mahendra Dhoni top-scored with a slow 58 before being the last man out as injury-hit Australia stamped their class on the match.
EARLY JOLTS
India frittered away advantage in both batting and bowling.
Left-arm Zaheer Khan had stand-in skipper Adam Gilchrist caught at slip for nought and Shanthakumaran Sreesanth removed Brad Hodge for three runs.
Michael Clarke (27), who hit a career-best 130 in Bangalore, led the early recovery before Symonds took centre stage.
Hayden hit five fours and three sixes until he was bowled by left-arm Irfan Pathan, the only bowler to escape punishment while returning two for 47 off 10 overs.
Symonds bludgeoned nine fours and two sixes facing 83 balls and joined forces with Haddin, who hit eight fours and three sixes facing only 69 deliveries.
Symonds got into verbal exchanges with Sreesanth, who had him caught and bowled to claim three for 67.
Sreesanth made a run out appeal against Symonds after he walked down from the non-strikers' end to confront the bowler, who appeared to say something to Haddin after a delivery.
Sreesanth has been fined several times in the last year and was docked 25 per cent of his match fee and warned over his behaviour during the Twenty20 tournament.
Tendulkar and Uthappa took 18 runs off one over from Brett Lee but Clark took the pace off the ball to great effect with the fight ending once Rahul Dravid (31), who added 49 runs with Dhoni, was caught in the deep.
The third game will be played in Hyderabad on Friday.
Dhoni unhappy with bowlers
Smarting from an 84-run defeat, Indian captain Mahendra Singh Dhoni said the bowlers did not bowl well in the last 20 overs against Australia and made it obvious that he was not happy with the performance of his frontline spinners.
After Dhoni had inserted Australia, India seized early initiative by reducing the visitors to eight for two in the fourth over and then 66 for three in the 16th over.
After that, Matthew Hayden (75) and Andrew Symonds (87) took over and down the order Brad Haddin's (87 not out) late flurry propelled Australia to a commanding 306 for six in 50 overs.
"The pacers bowled well and gave us a good start but I think we did not bowl well during 30 to 50 overs once again and that made a lot of difference. I think we need to improve on this aspect," a dejected Dhoni said after the match.
India went into the match with two specialist spinners but while Harbhajan Singh went wicketless and conceded 57 runs in his 10 overs, Ramesh Powar gave away 30 runs in his five overs without any success.
Asked if he was happy with the show by the spin twin, Dhoni's terse reply was 'There is room for improvement'.
The skipper, who scored a fighting 58 even as wickets kept tumbling around him, did not spare the batsmen either and said they needed to be more patient on the slow track.
"I think the batsmen needed to apply themselves a bit more. It was a wicket where one needed to do that to score runs," he said.
"Unfortunately, our batting did not click. Hopefully we will do that in the next match," Dhoni said.
Dhoni's opposite number Adam Gilchrist was ecstatic at getting the result after the frustrating wash-out in Bangalore.
"It was a solid performance. We had a wash-out in Bangalore and it is fantastic to get a result here. It was a solid performance and the only area we let ourselves down was the top-order batting. Me and Brad Hodge didn't score again but otherwise it was a fantastic display," he said.
Gilchrist said the pitch was exactly the way the Aussies had expected, which helped them adapt better.
"This wicket is a bit similar to what we expect in India. And that helped us. We won today but there are still five more games to go," he said.
Coming into the series with a depleted squad, Gilchrist said he was impressed with the way last-minute inclusions proved themselves.
"As I have said before, with injury comes opportunity and the way these guys, who came into the side because of injuries to others, have performed is just fantastic," he said.
The wicket-keeper batsman praised Man of the Match Brad Haddin, saying, ‘Haddin is a great example of how one needs to convert opportunities. He got his chance and proved himself’.
On Ricky Ponting's injury status, Gilchrist said the regular skipper was on course for a comeback soon. Ponting has been out of action due to a hamstring strain.
"We are getting closer and closer," he said, when asked whether Ponting would return to the side for the third match in Chandigarh.
"I will be happy to have him back. We have got a couple of days to assess the situation," he added.