In a match of records, South African wicketkeeper AB de Villiers equalled Englishman Jack Russell's world best of 11 dismissals in a Test that came in the same ground in 1995.
Having set Pakistan, who made their lowest Test total of 49 in the first innings, an improbable 480-run victory target, South Africa bowled them out for 268.
The new ball did the trick as the visitors lost their final six wickets for 59 before the lunch break.
Steyn picked up five second innings wickets to finish with his fifth 10-wicket haul which also earned him the man-of-the-match award.
"With all the hype going into the game from a personal point of view I felt it was always important we won," South Africa captain Graeme Smith, celebrating his 100th Test as skipper, said.
"To win so comprehensively was even better.
"Day two we set a standard as a team when we bowled Pakistan out for 49, we must now feel we can achieve that level of performance more often."
Smith singled out Steyn's performance following the bowler's lengthy 10-over spell on Monday on his way to five wickets to go with six from the first innings.
"Dale was outstanding, it was important that someone set the tone for us with the ball and he did that. Everybody followed suit afterwards," said Smith.
Resuming on 183-4, Pakistan had added 26 runs to their total in the morning session before the first wicket fell.
Steyn managed to get a delivery to nip away from Asad Shafiq and the edge was pouched low down by Jacques Kallis at second slip. It brought to an end a fine innings of 56 in which Shafiq kept the South African pace attack at bay for 168 balls.
Shafiq and Misbah-ul-Haq had added 127 for the fifth-wicket, bettering the previous record against South Africa of 107 between the same two batsmen in Abu Dhabi in the 2010/11 season.
Misbah fell in Steyn's next over to a delivery that pitched on off-stump, moved away and caught the edge of the bat for a simple chance to de Villiers. He went for a well-constructed 64.
Sarfraz Ahmed (six) tried to leave a Vernon Philander delivery but only succeeded in getting an inside edge onto the stumps.
Umar Gul (23) and Saeed Ajmal (11) hit some lusty blows but it was only a matter of time before they succumbed, the latter gloving a ball to de Villiers as he tried evading a Morne Morkel bouncer.
Junaid Khan was bowled by Morkel off a no-ball, the second time in this match that a South African over-stepped when picking up a wicket after Vernon Philander did likewise earlier in the innings.
Gul became Steyn's next victim when he played a wild swish at a short ball and was caught by de Villiers. It was originally given not out, but overturned by the third umpire on review.
Steyn trapped Junaid Khan leg before for nine, capping a magnificent display of fast bowling that Pakistan will somehow have to counter in the next two Test matches in Cape Town (Feb 14-18) and Centurion (Feb 22-26).
"It is always difficult when you come to South Africa and right now they are the number one side in the world, they have the top bowlers and some of top batsman in the world," said Pakistan captain Misbah.
"It is a challenge for us. We bowled well, especially in the first innings, and our batting in the second innings was much better. We need to improve more and work out a way to get them out and stop them scoring runs. But we must take confidence from some aspects of this match," he added.