Earlier in the first session, Vijay and Pujara played with poise to help India post 193/2 in reply to Australia's 451 at lunch.
Pujara's 202, compiled over 525 deliveries, was the third double hundred of his career and second against the Baggy Greens, while Saha's third Test ton provided steely support.
Virat Kohli, when they beat England 4-0 in the five-match Test series, said he thought England were going to be their toughest opponents, and he was ecstatic at dominating Alastair Cook's men, but Australia have showed they are a much better Test team in these conditions.
Smith, the only two-time century maker on both sides, is averaging 87 and Renshaw is averaging 43 with a top score of 68. It was a long two days. Yet they never managed to break the Australians. It is the most overs delivered by an Australian in a Test innings since Jim Higgs' 79.4 overs against England in 1979. "Whatever they are doing, we take it as sportingly".
"All our bowlers bowled really well, but according to me it was Jadeja who was the standout performer", Kohli said.
"I think the hardness of the ball was a big factor", the 28-year-old told reporters at the Jharkhand State Cricket Association Stadium.
The pair shared a 199-run stand as the touring attack failed to take a wicket in either the morning or afternoon sessions. "Roles always reverse its not a big factor for us".
'I represent middle America': Tomi Lahren explains her brand on 'The View'
While Lahren did not call out anyone in particular, she stuck by her words following her " The View " appearance. The often controversial Tomi Lahren of TheBlaze joined the women of ABC's "The View" on Friday.
Peter Handscomb batted for most of the last day for an unbeaten 72 and shared a match-saving 124-run partnership with Shaun Marsh as Australia salvaged a draw Monday in the third test against India.
India is in a strong position heading into the final day of the third Test in Ranchi after declaring at 9-603 on Sunday. Pujara is only the fourth batsman to face over 500 balls against Australia.
Virat Kohli injury: While Kohli came out to field in the second innings, that shoulder is still bothering him - he only stood in the slips, to avoid having to dive or throw. We both use the same ball, you've just got to go what you can with it'.
Pujara was the beneficiary of a marginal lbw call, prompting Australia to review unsuccessfully as Steven O'Keefe looked to have beaten the inside edge of the bat, only for replays to prove inconclusive before the original decision was upheld. Surprisingly, in this Test match in Ranchi the crowd turn out has not been encouraging.
Everything suddenly looks blurry to me. The fast bowler from New South Wales hampered India's progress further, when Ajinkya Rahane (14) edged a wide delivery to the keeper. Is Glenn Maxwell really injured? I can no longer remember which one of us is Matt Renshaw, are we still out here playing cricket, or is this just a description of a bad Test match that a sports psychologist is telling us about while we're hypnotised to prepare us for India?
Having bowled so much, maybe Ashwin is just exhausted, and if it is that, it is perfectly understandable. Does Roquefort even have a rind?