Amla declared half an hour before the scheduled tea break but rain prevented the start of the West Indian reply.
Amla made 208 and the left-handed Van Zyl hit an unbeaten 101 on another day of suffering for a depleted West Indian bowling attack.
Left-arm spinner Suleiman Benn took the only two wickets to fall on Thursday, dismissing AB de Villiers for 152 and having Amla caught on the long-on boundary.
The West Indies were without fast bowler Kemar Roach, who left the field on Monday afternoon after injuring his right ankle.
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A team spokesman said scans had revealed no significant damage and it was hoped he would be able to bowl later in the match.
Roach's injury left the tourists with only three front-line bowlers, with Jerome Taylor and Sheldon Cottrell providing pace and Benn needing to tie up one end with spin.
There was early success when De Villiers sliced a flighted delivery from Benn to Jerome Blackwood at point, ending a South African Test fourth wicket record partnership of 308 with Amla.
The pair had come together at 57 for three after all three wickets fell without a run being added.