Steyn took 6-34 at the Centurion as West Indies crashed to 131 all out, after being 76-2 overnight.
Even allowing for an ankle injury to Kemar Roach, which has ruled the West Indian fast-bowler out of the rest of the series, the first of three Tests was a mismatch.
West Indian captain Denesh Ramdin admitted his side was only in the game for about an hour on the first day, when they reduced South Africa to 57-3. But they only took two more wickets, as South Africa piled up 552-5 declared, before their batting crumbled twice in less than a day and a half.
Leon Johnson's 39 in the second innings was their highest score of the match, leaving Ramdin rueing poor discipline. "I am disappointed the way the guys got out after making good starts," he said.
"South Africa are the number one team in the world and Steyn bowled a fantastic spell this morning. We need to be more disciplined against them, including myself."
Ramdin said he expected a better performance in the second Test in Port Elizabeth, starting on December 26. West Indies won in the coastal city on their previous tour seven years ago and the pitch is expected to be slower with less bounce than at the Centurion.
South Africa captain Hashim Amla, who was named man of the match after scoring 208, voiced some sympathy for his team's vanquished opponents. “The pitch quickened up a bit today and it can be difficult to bat here on days four and five. Any team in the world would have struggled to handle our attack today."
Steyn said the wickets of Chanderpaul and Samuels, the only West Indian batsmen with proven credentials, were crucial. "Those two are big players,” said Steyn. “That's not to say that the rest of the guys can't contribute, but we know those are the two wickets to get.”
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