Chawla (4/31) and Harbhajan (3/15) exploited the conditions to perfection and troubled all the Australian batsmen on a turning track at Chinnaswamy Stadium to earn a morale boosting victory for India.
Earlier, Indian batsmen failed to live up to expectations as they were bowled out for 214 in 44.3 overs after electing to bat. Senior batman Sachin Tendulkar and strike bowler Zaheer Khan did not play due to slight niggles.
Virender Sehwag top-scored with a 56-ball 54 while Yusuf Pathan made a 39-ball 32. None of the other top-order batsmen could make substantial contribute.
Chasing a modest 215 for a win, Australia were cruising at one stage on 118 for two before Chawla and Harbhajan cast a web around Ricky Ponting`s men to bowl them out for 176 in 37.5 overs in front of a packed crowd.
Surprise inclusion in the World Cup squad, Chawla proved his critics wrong and brought India back into the match with a double strike in consecutive deliveries in the 29th over and took two wickets later to play a huge role in India`s victory.
The leg-spinner was a revelation today as he extracted big turn from the track and varied his deliveries to unsettle the Australians.
Ponting, who returned to competitive cricket after a finger injury lay-off, top-scored for Australia with a hard-earned 57 that came off 85 balls after opening duo of Shane Watson (33) and Tim Paine (37) had given them a flying start.
Apart from the trio, no other top-order Australian batsmen could manage any significant score in the high-profile practice match.
S Sreesanth was impressive among the Indian pacers as he extracted considerable amount of pace and bounce from the lively track.
India play their second warm-up game against New Zealand in Chennai on February 16.
Watson and Paine gave an aggressive start to Australia`s run chase. They showed scant respect to the Indian pace trio of Ashish Nehra, S Sreesanth and Munaf Patel as they struck boundaries at will to bring up the team`s 50 in 44 balls.
Watson was the more aggressive between the two openers as he struck as many as seven fours during his 26-ball 33 run cameo before falling prey to Sreesanth.
He departed in search of one run too many. He tried to heave Sreesanth over mid-off but did not connect it well and an agile Chawla did the rest by taking a sharp running catch.
After Watson`s departure, Ponting joined Paine in the middle and duo played sensibly without taking any undue risks to raise Australia`s 100 in the 18th over.
Yuvraj Singh broke the 67-run second wicket stand when he had Paine holed out at long-on boundary to Munaf Patel, who took a good running catch.
Chawla gave another reason to rejoice for India when he bowled Michael Clarke for naught in the next over for his first wicket of the day. He then brought India back into the match with a double strike in consecutive deliveries in the 29th over.
The leg-spinner first picked up Cameron White, caught by R Ashwin at mid-off, and then had David Hussey stumped in the very next delivery but new man Callum Ferguson foiled his hat-trick chance.
He added another to his kitty when he induced an edge from Callum Ferguson, who looked out of sorts against spin, and Virat Kohli did the rest in the first slip after giving the batsman a life in the previous over.
Harbhajan Singh, who had a quiet day in office till then, joined the party and accounted for two Australian batsmen -- well-set Ponting and Mitchell Johnson, both stumped by Dhoni in consecutive overs.
From there on, victory for India was just a matter of time and Harbhajan made it easier when he caught Jason Krejza plumbed in front of the wicket and then Ashwin completed the formality with the wicket of Lee.
Earlier, an impressive Brett Lee produced a fast and furious second spell to skittle India out for a modest 214.
Lee (3/35) accounted for three Indian wickets in his second spell of five overs, giving away just 12 runs. He was ably supported by John Hastings who returned with figures of two for 24 from his six overs.
David Hussey also picked up two wickets during the fag end of the Indian innings with the part-time off-spinner giving away 25 runs.
India produced a listless batting display as they lost wickets at intervals.
Apart from Sehwag, the Indian batsmen were found wanting from the outset against Australia`s lethal pace battery. Virat Kohli (21), skipper Mahendra Singh Dhoni (11) and Suresh Raina (12) all got starts but gave away their wickets when the team needed them.
India`s agony in the batting department can be gauged from the fact that they failed to notch up a single 50-run partnership, the highest being the 49-run ninth wicket stand between Pathan and R Ashwin (25 not out).