Connect to share and comment
Steyn dismissed overnight batsmen Asad Shafiq and Misbah-ul-Haq inside his first three overs with the new ball to sweep away the last serious resistance by the tourists.
He also took the last two wickets to finish with five for 52 and match figures of 11 for 60.
Wicketkeeper AB de Villiers held five catches to add to the six he took in the first innings.
He also became the first player in Test history to make a century and claim ten or more dismissals in a match after hitting an unbeaten 103 in the second innings.
Graeme Smith, captaining a South African Test side for the 100th time, said his men had achieved a peak of excellence on the second day when they bowled out Pakistan for 49 and then stretched their lead beyond 400 with solid batting.
"Day two was the standard," he said. "We reached the height that we can achieve as a team." Staying at that level was the challenge.
"To keep backing up performances is the key for us. We have to focus on keeping standards high."
Shafiq's dismissal ended a stubborn fifth wicket stand of 127 with Misbah. The pair added 20 runs to the overnight total of 183 for four in the five overs that had to be bowled before the new ball could be taken.
Only another four runs were added before Steyn had Shafiq caught at second slip by Jacques Kallis for 56 in the third over with the new ball. Shafiq had faced 168 balls and hit nine fours
In his next over Steyn had Pakistan captain Misbah caught behind for 64, made off 167 balls with 11 boundaries.
Sarfraz Ahmed chopped a ball from Vernon Philander on to his stumps and Saeed Ajmal provided De Villiers with his tenth catch of the match when he gloved a lifting ball from Morne Morkel to the wicketkeeper.
There was some frustration for the bowlers as Umar Gul slogged his way to 23 and Morkel was denied a wicket after bowling Junaid Khan when a replay showed he had sent down a no-ball.
But Steyn had Gul caught behind and then trapped Junaid leg before wicket with the fourth ball of the last over before lunch.
Misbah said Pakistan needed to find a way to deal with South Africa's fast bowlers.
"We have to give credit to the South African bowlers, especially Steyn. He took the game away from us," said Misbah.
"We have to work on how to handle the new ball and the outswinging deliveries. We have to negotiate that well. In the second innings we saw that when the ball gets old we can score runs."
There are ten days before the second Test in Cape Town and Misbah said the batsmen would practice hard against the new ball.