Faulkner, who came to bat with Australia six down at 213, soon turned the tide in favour of the visitors and slammed an unbeaten 64 off 29 balls to secure a sensational victory. He hit two boundaries and six dazzling sixes during his fearless knock.
He was adjudged man of the match for his brave effort.
It was Australia's highest ODI run chase on the Indian soil.
Voges, on the other hand, remained not out after scoring 76.
After a fighting fourth wicket stand, that rescued the visitors from 88/3, Australia lost skipper George bailey, Glenn Maxwell and Brad Haddin in quick succession and were reduced to 213/6.
Voges shared 83-run stand with George Bailey (43) before the skipper was trapped leg before by Vinay Kumar in the 37th over.
Shikhar Dhawan's brilliant throw then got Glenn Maxwell (3) run out, reducing the visitors to 174/5.
Bailey and Adam Voges helped Australia recover from early blows and took the score past 150 in 33 overs.
After a solid 68-run opening stand, Australia lost both openers Phillip Hughes, Aaron Finch and Shane Watson in quick succession to get reduced to 88/3 in 19.1 overs.
Vinay Kumar gave India first breakthrough in the 13th over by getting Phillip Hughes (22) caught behind after a good first-wicket stand.
Pacer Ishant Sharma then struck in the 17th over to send back Australian opener Aaron Finch after his gritty knock of 38, giving Australia second blow.
Finch (38 off 44 balls) was trapped leg before wickets by Ishant at the score of 82.
Ravindra Jadeja then joined the party by dismissing Shane Watson. Watson was trapped leg before after scoring 11.
Earlier, skipper MS Dhoni led from the front by smashing an unbeaten 139 as India recovered from a poor start to score a huge total.
Dhoni rescued India after early jitters as he played a responsible and sensible innings that came off just 121 balls, including 12 fours and five sixes.
The skipper also shared two significant partnerships -- putting on a solid 72-run stand for the fifth wicket with Virat Kohli (68) before joining hands with Ravichandran Ashwin (28) to put up 76 runs for the seventh wicket.
For Australia, Mitchell Johnson was the pick of the bowlers with figures of four for 46.
Put in to bat, India did not make an ideal start as openers Rohit Sharma (11) and Shikhar Dhawan (8), both of whom were instrumental in setting up a great platform for the team's massive 360 run chase in the previous game, today fell cheaply.
With India two down for 37, the onus was on Suresh Raina and Kohli to bail the hosts out of trouble.
But in the 13th over, Johnson struck back to see off Raina caught at the slip by Shane Watson before dismissing comeback man Yuvraj Singh off his very next delivery for a first-ball duck.
It was heartbreak for the fans of local hero Yuvraj, who edged an away going delivery to wicketkeeper Brad Haddin.
Raina and Yuvraj's dismissals in consecutive balls led to the run flow drying up.
Both Kohli and Dhoni also adopted a cautious approach as the duo confined themselves to scoring just in singles and twos. There was no boundary or a six hit for as many as eight overs.
Kohli broke the shackles in the 24th over and slowly but steadily completed his half-century to help the team rebuild.
Although Kohli and Dhoni failed to accelerate the scoring rate, they kept the scoreboard ticking before Glenn Maxwell returned the latter for a patient 68 off 73 balls, laced with nine fours.
Johnson then left the hosts reeling at 154 for six with all-rounder Ravindra Jadeja's wicket.
With the top and middle-order back in the pavilion, Dhoni showed a lot of character as he played with responsibility. He waited patiently for the loose deliveries to go for the fours and sixes.
Dhoni, mostly picked on James Faulkner and Watson. He began an over of Faulkner with two consecutive fours and then topped it up with a boundary and a six in Watson's over to release the pressure.
In the able company of Ashwin, he took India beyond the 200-run mark.
He tried to keep the strike so that the lower order had to face lesser number of balls. And almost single-handedly guided the team to a 300-plus total in the end.
Dhoni stole 21 runs in the last over, which was bowled by Faulkner.
He played his trademark helicopter shot to the delight of the packed PCA stadium crowd before hitting another six over the long off and a four to end the over.
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