The 27-year-old claimed seven wickets in India's second innings and 12 for the match to take the home side to a thrilling triumph after Australia had set the tourists 364 runs for victory on a rollercoaster final day on Saturday.
"Nathan Lyon has produced the most emphatic spin bowling performance by an Australian since the retirement of the great Shane Warne," wrote Sydney's Daily Telegraph.
"In a career-defining match for the much-maligned offie, Lyon exorcised his demons from two years ago against South Africa on the same ground in a huge boost for Australia looking ahead to next year's Ashes.
The Australian said Lyon's heroics were a "coming of age", and praised him for overcoming the widely held concern that he has been unable to finish off matches when needed.
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"A lot of ink has been spilled on this subject and there was a lot being ordered for (Sunday's) pages if things had not turned out as they did," the newspaper said.
Lyon's persistence against the Indian batsmen and umpires also drew comparisons to the late, great South Australian off-spinner George Giffen.
"Lyon's match figures of 12-286 off 70.1 overs were a perfect replica of a Giffen performance," Melbourne's The Age wrote.
"Graciously, Lyon complimented umpire Erasmus and explained, 'I just had to keep asking the question.' Eventually, he got his answer, and cricket got the Test match it wanted."
Australia's second Test against India starts on December 17 in Brisbane.