Resuming on 253 for five, Misal and Bandekar, who had already stitched 97 runs for the sixth wicket, extended the partnership to 111 runs together before the former got out.
Misal's knock saw him hitting 10 boundaries, while Bandekar also sent the ball 10 times to the fence, besides going for the maximum once.
Yesterday, Kamat had scored a half-century.
Services' Suraj Yadav (4/92), Deepak Punia (3/62) and Roshan Raj (2/83) were among wickets.
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In reply to Goa's first innings score, Services got off to a poor start losing both their openers for 10 runs on the board. Gauresh Gawas (2/11) claimed both the wickets.
At the close of play, Anshul Gupta was batting on 13 and skipper Rajat Paliwal was on nine.
Services still require 277 runs with eight wickets in hand to overtake Goa's first innings total.
Goa 1st inngs: 304 all out in 99.1 overs (Darshan Misal 76, Saurabh Bandekar 84; Suraj Yadav 4/92, Deepak Punia 3/62).
Services 1st inngs: 28 for 2 in 10 overs (Gauresh Gawas 2/11).