Parkar (5 for 32) was well-supported by senior pace colleague Dhawal Kulkarni (3 for 67) as the hosts made a strong bid to gain full points in their must-win game for a berth in the knock-out rounds.
However, Tripura hit back strongly before close by reducing the 41-time champions to 77 for three, with opener Jay Bista going strong on 43 to renew the battle tomorrow.
The 23-year-old Parkar was rewarded for a disciplined line and length on a track which had bounce. He missed a hat-trick in his 15th over, when he removed Tripura's highest scorer Mura Singh (43 off 62 balls) and Rana Dutta (0), both caught by Surya Kumar Yadav.
Parkar, who made his Ranji Trophy debut this season itself against Madhya Pradesh, was the pick of the bowlers. He wreaked havoc by first cleaning up Bishal Ghosh (32 off 37) and later castled wicket-keeper S K Singh (18).
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To add to his woes, Thakur also injured his left shoulder when dropping a catch just before tea and has gone for an MRI, according to a team official.
At tea, Tripura were tottering at 186 for 8 and, after the break, Mumbai grabbed the final two wickets in quick succession to end Tripura's innings in just 60.4 overs.
For the visitors, apart from Mura Singh, Bishal Ghosh and Yashpal Sharma (33) failed to convert their starts. Sharma too was one of Parkar's victims when he edged to wicket-keeper Tare.
In reply, the hosts lost their in-form opener Prithvi Shaw (1) and one down Shreyas Iyer (1) cheaply. While Prithvi was cleaned up when he tried to play an attacking shot by Rana Dutta, Iyer edged to the keeper after the ball rose on him off Mura Singh.
After that, Bista and Yadav stitched a 50-run stand for the third wicket before the latter threw away his wicket, caught and bowled by Abhijit Sarkar.
Bista and Karsh Kothari (1 not out) ensured no more damage was inflicted by the Tripura bowlers as the hosts ended the day 118 runs adrift of the visitors' first innings tally.
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