The 31-year-old bowler flummoxed the Australians in a sensational spell of slow bowling which saw him miss out on hat-tricks twice in the dead rubber as Australia have already clinched the series 4-1.
He dismissed Brad Hodge (16) and Andrew Symonds off the last two balls of the 20th over before returning to send back Brad Haddin (19), Brad Hogg and Brett Lee in the 32nd.
James Hopes (22) became the sixth victim of the bowler who was picked midway through the series after 20 months in wilderness.
Kartik's figures just fell short of the best-ever by an Indian spinner, a record held by Anil Kumble who took 6 for 12 against West Indies in Kolkata in 1993.
Captain Ricky Ponting top-scored with 57 off 78 balls with nine fours and shared two half-century stands with Adam Gilchrist (19) and Hodge to lend respectability to the total after electing to bat on a lively wicket.
The visitors got away to a poor start, losing Michael Clarke off the very first ball by left-arm seamer Zaheer Khan.
Ponting though looked in glorious touch, racing to his half-century with the help of nine fours to become the first one-day captain to score 50 fifties. New Zealand's former captain Stephen Fleming is second in the list with 45.
Hodge failed yet again to find form when he offered a tame catch in the slips while Symonds, who had smashed an unbeaten 107 in the previous game at Nagpur, was caught by Sachin Tendulkar.
Symonds, in the news for his run-ins with Indian players and allegedly being the target of racial abuse during the fifth game at Vadodara, was booed by the 40,000-strong crowd as he made his ground.
Former Indian captain Rahul Dravid was dropped for only the second time in his career following his prolonged form slump. In the last nine innings, the batsman averaged 8.8 with three ducks.
Paceman Shanthakumaran Sreesanth was replaced by Rudra Pratap Singh while Australia remained unchanged.