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Morkel finished with four wickets for 116 runs from 34.1 overs, as West Indies were dismissed for 546 about 45 minutes before the rescheduled close, replying to the South Africans' first innings total of 543 for six declared.
Graeme Smith and Alviro Petersen then batted through the remaining time to carry the Proteas to 23 without loss at the close on the fourth day at Warner Park.
Morkel had removed the first two West Indies wickets, and returned to mop-up the tail, when he removed Ravi Rampaul caught behind for 31 to give wicketkeeper Mark Boucher his 500th victim in Tests, and Sulieman Benn caught at second slip for 26.
The lanky fast bowler's intervention was not swift enough however, after Rampaul and Benn endured a one-and-a-half hour break delay after tea to complete a 59-run stand for the ninth wicket to further frustrate South Africa.
Before lunch, the South Africans were made to endure the slow grind from Chanderpaul and Bravo, which was interrupted by a 16-minute break for rain.
The Proteas' bowlers endured a fruitless toil, as West Indies reached 463 for four at lunch, after they continued from their overnight total of 424 for four.
South Africa's bowlers were hamstrung by the docile pitch, and Chanderpaul and Bravo showed no great urgency in gathering runs.
The closest the South Africans came to buying a wicket came in the first half-hour, when Bravo edged a delivery from Dale Steyn between slip and gully for his second boundary.
But the Proteas snared four wickets - two to left-arm spinner Paul Harris - to bring the Test back to life before tea.
South Africa hit a rich vein, as West Indies slipped to 502 for eight at the break.
Harris struck, when he held a return catch to dismiss Shivnarine Chanderpaul for the top score of 166, then had Dwayne Bravo caught behind for 53 to finish with two for 165 runs from 62 overs.
This was a purple patch for the South Africans, as West Indies slipped from 471 for four to 486 for eight.
Chanderpaul, whose innings included 10 fours and one six from 357 balls in just over eight hours, and Bravo added an even 100 from 330 balls for the fifth wicket.
In between Harris' two scalps, Lonwabo Tsotsobe allowed Bravo the luxury of his fourth boundary with a back-foot square drive to reach his 50 from 176 balls, and gained the scalp of Denesh Ramdin caught at backward point for one, and Jacques Kallis had Shane Shillingford caught at second slip for seven.
South Africa lead the three-Test series 1-0, after they won the first Test by 163 runs inside four days last Sunday at Queen's Park Oval in Trinidad.
