Young firebrand Quinton de Kock (48 not out) and Faf du Plessis (37 not out) put on 83 in 73 balls for the second wicket as the Proteas coasted past their victory target in 14.3 overs.
Magnificent swing bowling from Steyn and Tsotsobe had Pakistan reeling at three wickets down with just four runs on the board after Mohammad Hafeez had won the toss and elected to bat.
Umar Akmal (49 from 41 balls) brought a semblance of respectability to the score before he was run out near the end of Pakistan's innings, with the next highest score Shoaib Malik's 12.
Imran Tahir picked up two for 17, both his wickets stumped by De Kock, as Pakistan charged at everything despite their perilous situation.
Having won the one-day series 4-1 recently, the South African batsmen have established the ascendancy over Pakistan's bowlers in the UAE and it never looked like their target that would trouble them.
Hashim Amla (13) lost his leg-stump to Sohail Tanvir, but a career-best knock from the exciting De Kock, who was ably supported by Du Plessis, brought victory in quick time.
The second Twenty20 international will be played at the same venue on Friday.
(Reporting by Nick Said in Cape Town; editing by Ed Osmond; nick.said@thomsonreuters.com +27832722948 Messaging nick.said.thomsonreuters.com@reuters.net; To sign up for our Global Sports Forum chatroom, click on https://forms.thomsonreuters.com/global_sports_forum)
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