Rahane has led the side with aplomb, making best use of the sparse resources at his command.
Thakur, playing his second Test, emerged as India's unlikely batting hero, top-scoring with a counter-attacking 67 to deny Australia a substantial first-innings lead on Sunday.
Having finally bowled India out for 336, Australia finished day three on 21 for no loss, an overall lead of 54 in the series decider.
Rohit looked in good touch during his 44 off 74 balls but was dismissed trying to loft Lyon over mid-wicket.
The Indian opener was seen limping immediately after holing out to long on just before tea on the second day of the fourth and final Test at the Gabba.
Australia made 369 in the first innings of the series-decider at the Gabba.
Australia exploited India's injury woes and punished their poor fielding to reach 274/5 at the close of a steamy opening day of the fourth Test.
The pacer forced off the field during the second session of the opening day due to groin pain and taken for scans.
The left-arm pacer, who came to Australia as a net bowler, became the first Indian cricketer to make his international debut across all three formats during the same tour.
India will give their walking wounded every chance to prove their fitness for the series-decider, batting coach Vikram Rathour said.