Christopher Barnwell and Sherfane Rutherford then provided some foundation for the Jaguars innings with a 58-run partnership before Rutherfod fell for 22. Barnwell fell right after for 36.
Veerasammy Permaul and Shepherd then added 36 together before the last 2 wickets fell.
Guyana Jaguars all out for 158 from 47.1 overs. Bowling for Kent CCC, Will Gidman finished with figures of 4/20 from 10 overs.
Kent Spitfires looked set to finish the match, as openers Daniel Bell-Drummond and Zak Crawley were blasting the ball to the boundary around the Coolidge Cricket Ground.
The total reach 57 before Devendra Bishoo got the breakthrough when he removed Zak Crawley for 28.
Romario Shepherd then had Bell-Drummond caught for 26 in the very next over and no further addition to the total.
Sean Dickson and Alex Blake then bolstered the Spitfires middle innings, with a partnership of 37.
Kent then lost two quick wickets but will Gidman and James Tredwell on 29 not out and 12 not out, respectively got their team to the required target of 159.
Kent CCC finished the match on 162/7 in 37 overs. Devendra Bishoo was the pick of the Jaguars bowlers with figures of 4/35.
Will Gidman was Man of the Match for his 29 not out and 4/20.