Morkel captured a career-best four for 21 and Langeveldt took three for 30 as the South Africans successfully defended a victory target of 225 to win the match at Windsor Park.
The victory gave the Proteas an unbeatable 3-0 lead in the five-match series, following a 66-run victory in the rain-marred opening match last Saturday at Antigua, where they also won the second game by 17 runs on Monday.
Scoreboard
SOUTH AFRICA
Amla b Benn 34
Smith lbw DJ Bravo 29
Kallis c Sammy b Benn 31
De Villiers (run out) 70
Petersen b Pollard 16
Miller c Ramdin b Taylor 5
Botha c & b DJ Bravo 18
McLaren c Richards b Pollard 5
Steyn b Rampaul 0
Morkel c DM Bravo b Pollard 14
Langeveldt (not out) 0
Extras (LB-2) 2
Total (all out, 47.2 overs) 224
Fall of wickets: 1-53, 2-91, 3-113, 4-153, 5-162, 5-197, 6-206, 7-207, 8-207, 9-223.
Bowling: Taylor 8-0-39-1, Ravi Rampaul 10-0-45-1, Suleman Benn 10-0-43-2, Dwayne Bravo 8.2-0-40-2, Sammy 5-0-28-0, Kieron Pollard 6-1-27-3.
WEST INDIES
Gayle c Kallis b Langeveldt 16
Richards c Kallis b Morkel 28
Chanderpaul c de Villiers b Kallis 24
DM Bravo lbw Morkel 1
DJ Bravo c de Villiers b Steyn 13
Pollard c Petersen b Langeveldt 10
Sammy c de Villiers b Langeveldt 14
Ramdin (not out) 15
Taylor (run out) 0
Benn c McLaren b Morkel 17
Rampaul c Botha b Morkel 7
Extras (B-4, LB-3, W-5) 12
Total (all out, 38 overs) 157
Fall of wickets: 1-29, 2-59, 3-63, 4-87, 5-93, 6-116, 7-118, 8-118, 9-147.
Bowling: Dale Steyn 7-1-19-1, Charl Langeveldt 7-0-30-3, Ryan McLaren 5-0-34-0, Morne Morkel 7-0-21-4, Johan Botha 6-0-29-0, Jacques Kallis 6-0-17-1.