The 22-year-old batter became only the fifth uncapped player in IPL history to score over 500 runs in a season
The hosts, replying to Australia’s first innings total of 478, went to tea on the third day at 314-2 with Tendulkar unbeaten on 148 and Vijay on 118.
Tendulkar and Vijay put on a record 276 runs for the unbroken third wicket after the hosts had been reduced to 38-2 in Sunday’s final session at the Chinnaswamy stadium in Bangalore.
It is the highest third-wicket partnership in India-Australia Tests, surpassing the 222-run stand between Aussies Allan Border and Kim Hughes in Chennai in 1979.
Tendulkar, who has also hit a record 46 one-day hundreds, has so far slammed 17 boundaries and two sixes in his latest century.
The Mumbai batsman, stuck in the eighties for almost 45 minutes, moved into the nineties by driving off-spinner Nathan Hauritz through the covers to also bring up India’s 200.
He then smashed Hauritz over long-on for six to reach 99 and repeated the shot in the bowler’s next over to complete his century to loud cheers from 15,000 home fans.
Vijay, playing the Test only because Gautam Gambhir was ruled out with a knee injury, spent an hour in the nineties before reaching his hundred with a single midway through the afternoon session.
The Tamil Nadu opener has hit 11 fours and a six as the bat dominated the ball on the easy-paced wicket.
Australia are seeking a series-levelling win after losing the dramatic first Test in Mohali by one wicket.
Tendulkar, who resumed at 44, reached his 58th Test half-century in the day’s first over with two pedal-sweep boundaries off Hauritz.
At the other end, Vijay drove Mitchell Johnson through the covers to bring up the 100-run partnership with Tendulkar.
Vijay survived an anxious moment when he was on 49 as he charged down the wicket, but a direct throw from Hauritz narrowly missed the stumps.
Tendulkar was severe on Johnson, flicking him to fine-leg before pulling the next ball for another boundary.
The duo scored 60 runs from 14 overs in the first hour, but an accurate spell from debutant fast bowler Peter George after the drinks break slowed down the run-rate.
The lanky South Australian, who conceded 18 runs in five overs late on Sunday, gave away only 12 runs in his five overs in the morning session.
Vijay returned after lunch to smash Hauritz for a straight six, signalling the 200-run stand for the third wicket.
Australia went wicketless in the first two sessions, with Hauritz being the most expensive bowler with 0-115 from 29 overs.
The 22-year-old batter became only the fifth uncapped player in IPL history to score over 500 runs in a season
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