The win was Jamaica’s second of the competition after beating Barbados in the opening round a fortnight ago.
Andre McCarthy top-scored with 45 from 65 balls while captain Tamar Lambert, voted Man-of-the-Match, chipped in with an important 34 and all-rounder David Bernard Jr, 28.
Seamer Raymon Reifer finished with two for 25.
Earlier, CCC were dismissed for 152 off 48 overs after winning the toss and batting.
Raymon Reifer got 32, captain Kyle Corbin scored 24 and Nicholas Alexis, 20.
Out-of-favour West Indies left-arm spinner claimed three for 27 while fast bowler Andrew Richardson (2-22), leg-spinner Odean Brown (2-27) and off-spinner Tamar Lambert (2-39) were the other wicket-takers.
CCC slipped to 15 for two in the seventh over after seamer Andrew Richardson removed both openers cheaply.
Veteran left-hander Floyd Reifer, who hit the top score of 32, and captain Kyle Corbin, who struck 24, then repaired the innings with a 55-run third-wicket stand before CCC lost their last seven wickets for 87 runs.
Jamaica were floundering after eight balls of the innings in their reply before two critical partnerships put them over the line.
McCarthy, who hit four fours and two sixes, and opener Simon Jackson (21) put on 56 for the third wicket while Lambert and Bernard added a further 47 runs for the fifth wicket, to put Jamaica in sight of victory.
CCC innings
C. Walton c Lambert b Richardson 6
S. Thomas c wkp. Baugh b Richardson 6
K. Corbin stp. Baugh b Miller 24
F. Reifer lbw b Brown 32
R. Reifer c Miller b Brown 15
N. Alexis c Bonner b Lambert 20
N. Parris c Bonner b Miller 11
A. Dewar c McCarthy b Miller 9
K. McClean lbw b Miller 5
D. Davis not out 14
R. Austin run-out 5
Extras: (lb-2, w-8) 10
Total: (all out, 48 overs) 157
Fall of wickets: 1-12, 2-15, 3-70, 4-78, 5-111, 6-114, 7-129, 8-134, 9-148.
Bowling: Richardson 7-1-22-2, Cotterell 4-0-11-0, Bernard 5-0-18-0, Miller 10-3-27-3, Brown 10-2-27-2, Lambert 10-0-39-2, McCarthy 2-0-11-0.
JAMAICA innings
J. Blackwood c F Reifer b McClean 0
S. Jackson c wkp. Walton b R Reifer 21
N. Bonner lbw b Davis 0
A. McCarthy lbw b Austin 45
T. Lambert c Davis b R Reifer 34
D. Bernard Jr Corbin b Dewar 28
C. Baugh not out 18
N. Miller not out 1
Extras: (lb-1, w-10) 11
Total: (6 wkts, 45.2 overs) 158
Fall of wickets: 1-0, 2-1, 3-57, 4-77, 5-124, 6-157.
Bowling: McClean 9-1-38-1, Davis 7-1-35-1, Austin 10-1-21-1, R Reifer 8-0-25-2, Dewar 9.2-0-27-1, Parris 2-0-11-0.
Points: Jamaica 4, CCC 0.