Having taken 6-8 in the first innings, Steyn finished with figures of 5-52 in the second as Pakistan was bowled out for 268.
A century stand between Misbah-ul-Haq and Asad Shafiq had given Pakistan the slightest glimmer of hope in its chase of 480, but the second new ball banished any chance of a record-breaking win on the fourth morning.
Steyn dismissed both Misbah and Shafiq, before claiming the final two wickets of the innings, giving South Africa a 1-0 lead in the three-match series.
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