With this win, they advance to Qualifier 2, where they will face Paarl Royals on Thursday night at the same venue.
Batting first, Sunrisers posted a solid total of 184/6, thanks to a captain's knock from Aiden Markram.
The skipper led from the front, scoring 62 off 40 balls, including five fours and two sixes. He found crucial support from Marco Jansen, who smashed 23 off 12 balls in a late flurry, adding 38 runs in the final two overs alongside Markram.
David Bedingham (27) and Tristan Stubbs (26) also chipped in with vital contributions.
In response, Joburg Super Kings faltered despite a promising start. They reached 49/1 in the first Powerplay but struggled to maintain momentum.
Jonny Bairstow (37) provided some resistance before being bowled by Liam Dawson, while Devon Conway (30) was dismissed early by Jansen.
Captain Faf du Plessis (19) and debutant JP King (9) failed to anchor the innings, and with 94 runs needed in the last seven overs, Joburg's chase crumbled.
The Sunrisers' bowlers dominated, with England's Craig Overton (2/20), Ottneil Baartman (2/25), Richard Gleeson (2 wickets), and Liam Dawson (2/35) dismantling the opposition.
With MI Cape Town having already booked their place in Saturday's Betway SA20 Final, it is now the turn of Sunrisers Eastern Cape and Joburg Super Kings to battle it out in the Eliminator at Centurion today.
Afghanistan's star leg-spinner, Rashid Khan, has set a new milestone in T20 cricket, surpassing Dwayne Bravo to become the format's highest wicket-taker.
The fourth edition of the SA20 tournament is scheduled to begin on December 26 this year.
MI Cape Town underlined their status as the Betway SA20 table-toppers for Season 3 with a comprehensive bonus-point victory over the Pretoria Capitals to close out a perfect record at Newlands on Sunday.
