South Africa claimed 6-85 on the fourth day on Monday to end up winning the Test by a commanding 211 runs. Steyn took another 5-52 from 28.4 overs in Pakistan's second innings to finish with match figures of 11-60.
Wicket-keeper AB de Villiers also took a South African record 11 catches over the two innings to go with his unbeaten 103 in the Proteas' second innings that was the only century of the match.
Pakistan did stage somewhat of a fight back late on the third day with captain Misbah-ul-Haq and Asad Shafiq combining for an unbeaten stand of 101 to move the tourists to 4-183.
That was only after Pakistan was bowled out for its Test record low of 49 in the first innings, though, with South Africa making 253 and then 3(dec)-275 to set the tourists 480 to win in the fourth innings of the match.
While coming into the fourth day the win and even the draw looked decidedly unlikely, Pakistan did have the chance to bat for a significant amount of time and really make South Africa's bowlers work for the last six wickets, but that's not quite how it ended up transpiring.
Misbah and Shafiq came together with Pakistan 4-82 in the second innings and did well getting to 4-183 at stumps, but South Africa got the second new ball five overs into the fourth day's play and it didn’t take long for the wickets to start to fall.
Shafiq was first to fall for 56 when caught by Jacques Kallis off Steyn. His innings was a gutsy one lasting 168 deliveries and almost four hours at the crease in his 17th Test.
Pakistan was then 5-209 and then 6-210 just two overs later when Misbah joined Shafiq back in the pavilion for 64 from 167 balls in 258 minutes.
The captain was caught behind by de Villiers off Steyn and ended any hope of a big, long Pakistan innings.
Vernon Philander then got in on the fun to bowl Sarfraz Ahmed for six, but Umar Gul and Saeed Ajmal didn’t give up their wickets easily. The pair put on 22 for the eighth wicket before Ajmal was also caught behind by de Villiers, this time off Morne Morkel for 11.
Gul then fell for 23 also caught behind off Steyn with Junaid Khan the final wicket to fall for nine when trapped LBW by Steyn. Rahat Ali remained not out on three.
As well as Steyn taking 5-52, Philander finished with 2-60, Morkel 2-89 and Kallis 1-35.
The Second Test of the three-match series begins in 10 days time on Thursday February 14 at Cape Town.