Cheteshwar Pujara and Ajinkya Rahane put up an unbeaten partnership of 93 runs as India ended third day's play at 213 for 4, with a lead of 126 runs.
Rahul, who top-scored with 90 in India's first innings, put on 45 with Pujara after Abhinav Mukund (16) was bowled by Hazlewood early in the lunch session.
Aiming at the stumps should be the way forward for Australia's quicks against India to take advantage of the uneven bounce on the M. Chinnaswamy Stadium pitch, fast bowler Josh Hazlewood said on Monday.
He finished with a magnificent figure of 6/63. Pujara felt India were still very much in the Test match, regardless, and hoped they could take the remaining wickets quickly. Their first innings lead was 87 runs.
The 29-year-old further expressed confidence that India would bounce back in this particular Test match and in the series. Pujara completed his half-century after tea, with India dominating the final session of the day.
Realising that they were not in the situation to go searching for wickets, India's bowlers opted to build pressure by stifling the flow of runs. The hosts had been bundled out for just 189 in the first innings.
Wade soon followed his overnight partner back to the pavilion after being trapped leg before by Jadeja, who then removed Nathan Lyon lbw next ball for a duck. As a effect, the first session fetched 2 wickets at the cost of just 47 runs.More news: Who Got Eliminated On The Bachelor 2017 Tonight? Week 9
While Jadeja claimed six for 63, Ashwin returned with a haul of 2 for 84.
Pujara said the pitch, while still offering the bowlers plenty of help, had probably been more hard to bat on on the first day, when KL Rahul had suggested Nathan Lyon profited from early dampness to generate extra turn and bounce.
All Hazlewood's wickets on Monday came when he attacked the stumps.
With the ball pitched wide, Rahul looked to go for an expansive drive, only to edge it to Smith who flew to his right to pluck the ball out of thin air.
By the time Rahul fell for 51, India's deficit was down to three runs. Pujara played 173 balls to hit six boundaries while Rahane also consumed 105 balls to hit three boundaries.
Providing the backbone for a team that had repeatedly failed to show any in previous outings in this series by posting an unbeaten 79 in nearly four hours at the crease. So, Aussie played nearly 16 overs in the first day and started to bat with all wickets in hand in second day at Bangalore.
Kohli reviewed the decision immediately and despite several replays, it could not be determined if he had hit the ball before it struck his pad and the umpire's decision was upheld.