In reply to the West Indies' 406, India's innings ended just after tea with Kaul remaining unbeaten. Mohammad Shami was the last man out, caught behind by Chadwick Walton off medium pacer Assad Fudadin for a handy 15 runs.
The wicketkeeper-batsman from Kangra fought hard to stay in the middle 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 and faced 148 balls during his dogged innings.
The West Indies attack was decent but could not capitalise, giving opportunity to the Indian tail-enders to stick around a defiant Kaul and reduce the lead.
Cummins bagged three for 58 and two wickets each were shared by Veerasammy Permaul, Nikita Miller and Assad Fudadin after they conceded 88, 77 runs and 23 runs, respectively.
Deonaraine took one wicket for 66 runs.
Even as the match seemed to be heading towards a draw, there is still enough interest left as Kirk Edwards and Powell, who have been picked for India and West Indies series, would like to be among runs before they get ready for the big challenge in November.