Kent 331 for 9 dec (Dickson 142, Crawley 62, Joseph 4-72) lead West Indians 265 by 66 runs
Sean Dickson hit an excellent 142 to ensure West Indies endured three sessions of leather chasing on the second day against Kent at Canterbury.
Kent declared in the final over of the day on 331 for 9 to secure a first innings lead over the West Indies of 66 runs going into the third and final day of the tourists penultimate warm-up game before the first Test with England starting on August 17 at Edgbaston.
Dickson, who amassed a career-best 318 against Kent's County Championship rivals Northamptonshire last month, cracked 29 fours and three sixes in his four-and-a-half hour stay that left the tourists wondering when their next wicket would come.
Dickson and first-class debutant Zak Crawley combined to post a record 182 for Kent's second wicket - beating the county's previous best against the tourists of 79 set by Brian Luckhurst and Alan Knott in 1969 - as the West Indies toiled all day for eight wickets.
Roddy Estwick, the West Indies bowling coach, was happy in the way his attack bounced back late on "A lot of our guys haven't really played in English conditions so they're still learning, trying to get their lengths right.
"If you look at Azzari Joseph, he got better as the day went along. He didn't start as well as we'd have liked, but we made one or two technical adjustments with his run up and we spoke about his lines, and he was able to look a lot better.
"I felt the figures of Miguel Cummins didn't do justice to the effort he put in and Bishoo didn't get any help of the wicket. But you have to credit Kent also, they batted nicely, they were patient and when the bad balls came along they put them away."
While Dickson, 25, took the plaudits, Crawley cut an impressive figure reaching a 94-ball 50 as Kent moved past the tourists' modest total of 265 all out soon after tea.
Crawley, 19 years-old and six feet six inches tall, played a mature and responsible knock full of well-timed drives and pulls as Kent, resuming on their overnight score of 1 for 1, dominated.
The pair set out to punish anything loose or wide as Crawley, a product of Tonbridge School, got off the mark on his first-class debut with a rasping pull for four through mid-wicket against Alzarri Joseph.
Dickson, making his first appearance for the county since the start of the NatWest T20 Blast, looked in good fettle from the off. His sweetly-timed punch drive flew past Joseph for four and he almost repeated the dose only to see the non-striker's stumps act as an inadvertent barrier.
The pair posted their half-century partnership inside 20 overs then Dickson upped the tempo by hitting the first six of Kent's reply just before lunch pulling a short one from leg-spinner Devendra Bishoo over the ropes adjacent to the St Lawrence lime tree.
Dickson twice edged balls from Joseph just short of the keeper, then nicked one through the slip cordon for four but the delivery from Raymon Reifer was called a no-ball.
Dickson went on to post the 12th first-class 50 of his career from 105 balls with seven fours to go with his maximum, but might have gone for 51 when Bishoo downed a stinging caught and bowled chance.
The pair ploughed on during the mid-session with Crawley cracking seven fours before he departed to a stunning diving slip catch by Kieran Powell.
Acting Kent skipper Sam Billings scored a typically impish 25 before being run out by Shai Hope's throw from the deep then Dickson's stay ended when he holed out to long off. In a wonderfully old-school display of sportsmanship, the West Indies' side lined up to shake Dickson's hand as he trudged off.
In the quest for quicker runs Adam Ball danced past one from Kraigg Brathwaite to be stumped and Will Gidman was bowled by Reifer.
Against the second new ball Adam Rouse missed an attempted sweep to be skittled by Brathwaite, Charlie Hartley fenced to second slip and Adam Riley had his off pole plucked out to give Joseph hard-earned figures of 4 for 72.
In the final over of the day Calum Haggett took a blow on the hand from Miguel Cummins sparking Kent's declaration.