Sharma and Jadeja put India on top against Australia despite Murphy five-for
Murphy justified his selection by claiming 5-82 on a spin-friendly track at the Vidarbha Cricket Association Stadium but India finished day two on 321-7 replying to Australia's below-par 177 in the first innings.
Jadeja, who claimed 5-47 with the ball on Thursday, raised 81 runs for the unbroken eighth wicket with Axar Patel (52) to drive home India's advantage.
"Even after getting set, you could not afford a lapse in concentration on this track," Patel said after India finished the day with a lead of 144.
"Jadeja and I told each other if we maintain our focus, we could help set a good total on this track."
It was a day of hard toil for the tourists but Murphy impressed with his relentless pursuit for wicket.
The 22-year-old had removed KL Rahul late on Thursday for his first test wicket and the bespectacled off-spinner struck twice in the morning session to keep India in check.
He dismissed Ravichandran Ashwin lbw for 23 and induced Cheteshwar Pujara (seven) into playing a sweep shot to a delivery way outside the leg stump to be caught at short fine leg.
Murphy removed Virat Kohli (12) with the first ball after lunch and Nathan Lyon bowled debutant Suryakumar Yadav (eight) through the gate but Rohit was unperturbed.
The opener lofted Murphy over mid-off for a four to bring up his hundred and took a single off the next delivery to level the scores.
Pat Cummins, armed with the second new ball, finally ended Rohit's fine innings by sending his off-stump cartwheeling.
Rohit, who hit 15 fours and two sixes in his stellar knock, could have fallen in the previous delivery but Steve Smith floored a catch in the second slip.
Jadeja was the wrecker-in-chief with the ball and the all-rounder tormented Australia with the bat too bringing up his 18th test fifty.
Smith grassed another catch in the final over of the day giving Jadeja a reprieve.
Australia batter Matt Renshaw missed much of the action with knee pain but was cleared to return to field after undergoing scans.
Delhi, Dharamsala and Ahmedabad host the remaining matches of the four-test series for the Border-Gavaskar Trophy.
