Carter anchored the Tridents' innings with a well-crafted 111 not out off just 68 balls that consisted of 10 boundaries and five sixes, while opener Dilshan Munaweera (42) was the second highest scorer.
It was all credit to the West Indian, who almost single-handedly took the team past 170-run mark, even as only three batsmen in the side could reach the double-digit mark.
Put into bat, Carter and Munaweera lifted the team after they were reduced to two for seven in the third over of the match itself, with opener Shane Dowrich (0) and one-down batsman Raymon Reifer (1) getting out cheaply.
Dropping Carter at 26 proved costly for the Cobras, as he stole two fours and a six in that very over of Justin Kemp.
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However, it was an unfortunate end to Munaweera's knock that came off 21 balls, studded with five fours and two sixes, as the Sri Lankan batsman was run out.
Carter, however, stuck to his guns at one end, although his new partners in James Franklin (3), Jeevan Mendis (10), Jason Holder (0), Ashley Nurse (0) and Akeal Hosein (6) were back to the dressing room in quick succession.
For Cobras, Sybrand Engelbrecht (2/24) and Charl Langeveldt (2/29) finished with two wickets each.