At the close of play on Day 2, West Indies A were 28 for no loss in their second innings, extending their overall lead to 75 runs.
Before Kaul's rearguard unbeaten knock of 64 off 172 balls, Vasudevan Jagadeesh (86) and Abhishek Nayar (89) were involved in a 99-run partnership for the fourth wicket, as India A were all out for 359 in their first innings.
Having gained slender lead, the West Indies A were at a pretty comfortable position at stumps with openers Kraigg Brathwaite and Kieran Powell batting on 18 and 9, respectively.
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.
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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.
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.