Australia's lead is just 16 runs, with Cheteshwar Pujara unbeaten on 164 and looking well placed to build a first-innings buffer for the hosts.
Pat Cummins, who again bowled with great quality for the tourists, had Saha given out lbw with his first ball of the day, but the batsman's referral showed the ball to be missing leg stump by millimetres.
But India captain Virat Kohli, absent from the game since diving on to his shoulder in the field early on day one, was unperturbed by the line-ball call, storming off his seat in the home team's room to sarcastically applaud Australia's misfortune. Pujara also went past 1000 runs against Australia, and for the fifth time, scored in excess of 150.
2 - 77 overs bowled by O'Keefe is the second most by any bowler since 2000 after 79 overs by Ray Price against SA in Bulawayo in 2001. Batting on 10 overnight, Pujara absorbed the pressure and built his innings beautifully as he struck his 11th Test century in a top class display of grit and gumption.
When the India one-day worldwide (ODI) squad then heads to England for the defence of the Champions Trophy, Pujara will once again stay behind, unless some English county is astute enough to acquire his services for a few Championship games. In the middle session, I think they had the better of us.
Pujara has always been spoken of as India's successor to the great Rahul Dravid, and while there are similarities in style and the way both use concentration and solid defence to grind down an opposition attack, Pujara still has a long way to go before he can be compared to India's greatest number three.
Cummins, who struck twice in the afternoon session, got Rahane caught behind and Hazlewood bowled Nair with a lovely reverse swinging delivery in the final session. "To produce some of the balls that he produced to get wickets was exciting", said Australia's assistant coach David Saker. It is also the most number of balls faced by a batsman in India.
With about half-an-hour left in the day's play, India declared their first innings at 603 for 9 with a lead of 152 runs. He was out stumped off Steve O'Keefe (1-117) in the last over before lunch.
Never the one to emulate his glamorous teammates, Pujara defies Australia with an undefeated ton as India reach 360/6 on Day Three.
(S.P.D. Smith 178 not out, G.J. Maxwell 104, M.T. Renshaw 44; R.A. Jadeja 5-124, U.T. Yadav 3-106).