At tea, Uday Kaul was unbeaten on 55 while Mohammed Shami was batting on nine, as India A trailed by 62 runs in reply to West Indies A's first-innings total of 406.
The wicketkeeper-batsman from Kangra fought hard to stay on the wicket as he saw wickets tumbling at the other end. The youngster came in when India were struggling at 245 for five.
Kaul struck four boundaries and a six off 148 balls in his dogged innings.
After the second drinks break, Deonaraine removed Parveez Rasool for 11 and right-arm Barbadian fast bowler Miguel Cummins struck a double blow by sending Bharghav Bhatt (11) and Zaheer Khan (0) to the pavillion.
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The West Indies A attack was good but could not capitalise, giving opportunity to the Indian tailenders to stick around a defiant Kaul and reduce the deficit.
Cummins bagged three for 58 and two wickets each were shared by Veerasammy Permaul and Nikita Miller.
Earlier, resuming at overnight score of 191 for three, Jagadeesh and Nayar began sedately but missed out on their centuries.
The unheralded Kerala opener Jagadeesh, who showed good temperament for his undefeated overnight score of 79, added only seven runs to his tally before being dismissed.
The youngster, who had also missed out on a century during the unofficial Test against New Zealand A earlier this year, had showed a lot of composure during his 198-ball knock that included eight boundaries.
Once Jagadeesh was packed off, Nayar (89) had to take a long walk back to the pavillion after he was trapped lbw by left-arm spinner Nikita Miller.