Lyon, who had dismissed Cheteshwar Pujara at the stroke of lunch, snapped two more wickets -- Virat Kohli (12) and Ajinkya Rahane (17) -- and O' Keefe accounted for Karun Nair (26) as Australia dominated the second session.
At the break, Rahul and Ravichandran Ashwin (5) were batting on 79 and 4, respectively.
The Indian opener, who was dropped at 30 and 61, hit nine boundaries in his 175-ball innings.
Kohli was surprised and consulted Rahul for the review, but replays showed that the ball had pitched outside off and the impact was in line and going on to hit the wickets.
At 88 for three, Rahane walked in the field and the very first ball he was greeted by a loud leg before appeal by Lyon and close-in Australian fielders, but umpire Long turned down the decision.
In 39.2 overs, India brought their 100 up when Rahul hit Lyon through mid-wicket region for a single.
Rahul was lucky as he was dropped by David Warner, who standing at leg slip, failed to hold on to the ball after the India opener miscued an attempted paddle sweep. He was then batting on 61.
In the 48th over, Lyon struck for the third time, removing Rahane. The Mumbaikar was stumped by Mathew Wade, who recovered in time after fumbling a bit initially.
Earlier, India were 72 for two at lunch with Lyon dismissing Pujara and Mitchell Starc sending back Abhinav Mukund for a duck.
Rahul had helped India recover from the early loss of Mukund, who was picked in the team at the last minute in place of an injured Murali Vijay.
The players walked off for lunch after Lyon's dismissal of Pujara in the 28th over at the M Chinnaswamy Stadium.
Coming off a humiliating defeat in Pune, India trail the four-match series 0-1.
While a confident Australia took off from where they left in the last game, removing Mukund for a duck in the day's third over.
Rahul and Pujara (17) added 61 runs in 25 overs to steady the innings. However, Lyon sent back Pujara when he got an inside edge and the ball lobbed up for Peter Handscomb to complete a catch at forward short-leg, tilting the scales slightly in favour of Australia after the first session's play.
Pujara did not look very comfortable during his stay in the middle, while luck smiled on Rahul, who got a reprieve on 30 by Handscomb.
Earlier, India skipper Virat Kohli won the toss and elected to bat.
Australia have named an unchanged XI, while India have brought in Mukund and Karun Nair. Mukund is making a comeback to the Test side after five and a half years, replacing Vijay, who suffered a last-minute shoulder injury.
Nair, who had scored a triple century in his last Test, also got a chance after India decided to drop Jayant Yadav for an extra batsman.
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