The pair rotated the strike easily and their 50-partnership came up off 110 balls.
Ishant Sharma joined Wriddhiman Saha in the middle. Pujara and Rahane put up an unbeaten partnership of 93 runs for the fifth wicket and this could possibly change the outcome of the match.
He pinned Rahane in front and this time the review went Australia's way.
Virat Kohli has managed just 40 runs (ave.10.00) in four innings in the series - his worst average in Tests, eclipsing the 13.40 (134 in 10 innings) vs England in England in 2014.
"Not much adjustment. It was a little easier than the first innings, when the pitch was damp and that's why it bounced a bit more". But his stay too was short lived as Hazalwood scalped him just after the Indian batsman had hit the Aussie speedster for a boundary down the leg. Pujara hit seven fours in his marathan 221 ball essay.
India ended its long resistance to using DRS in November, becoming the last Test nation to embrace the technology, but the move has not been without hiccups.
Hazlewood, who has the progressive figures of 3-57 in India's second innings, says the Test is evenly poised. The control % of Indian batsmen against Lyon in both the innings, however, was similar - 77.61% in the first and 77.16% in the second.
Three times in the series, the Indians are yet to cross 200 but Pujara is confident that they can put up a good total here.More news: La Liga results: Barcelona back at the top as Real Madrid stumble
The chaos started when skipper Steve Smith referred an lbw shout.
Cheteshwar Pujara looked strong at one end and was joined by Ajinkya Rahane at the other end.
In an interesting move, Jadeja walked into the field after the departure of Kohli. Starc and Hazlewood led the attack today.
After playing a second fiddle to Australia in the first two days, India fought back on the third day in Bangalore to establish a lead of 126 runs with six wickets in hand.
Australia's batsmen, particularly the half-centurions Matt Renshaw and Shaun Marsh, seemed to trust their defence against India's spinners more than some of India's batsmen had done on day one against Nathan Lyon and Steve O'Keefe.
Pujara said conceding only 197 runs and taking six wickets represented a strong showing from the bowlers.
At stumps, Matthew Wade and Mitchell Starc were batting on 25 and 14, respectively.