Steyn took a phenomenal three for 10 in four overs as the Spartans could only manage 142 for seven in pursuit of 158 for victory.
The win kept the Blitz in contention for the playoffs and they are now only two points off the third-placed Spartans.
CAPE TOWN BLITZ: Quinton de Kock (capt, wk), Janneman Malan, David Bedingham, Liam Livingstone, Aviwe Mgijima, Vernon Philander, Mohammad Nawaz, Wahab Riaz, Sisanda Magala, Dale Steyn, Anrich Nortje.
TSHWANE SPARTANS:Theunis de Bruyn, Dean Elgar, Roelof van der Merwe, AB de Villiers, Heinrich Klaasen (capt, wk), Pite van Biljon, Wiaan Mulder, Tom Curran, Morne Morkel, Lungi Ngidi, Lutho Sipamla.
Meanwhile a gem of an innings from Sibonelo Makhanya and a late flourish from Isuru Udana helped the Paarl Rocks recover from a tricky position to cruise to a five wicket win over the Jozi Stars at Imperial Wanderers Stadium.
It was the Stars seventh consecutive loss of the competition while the Rocks took outright lead at the top of the table.
JOZI STARS: Kagiso Rabada, Shoaib Malik, Rassie van der Dussen, Reeza Hendricks, Daniel Christian, Temba Bavuma (capt), Duanne Olivier, Lizaad Williams, Ryan Rickelton, Aaron Phangiso, Sinethemba Qeshile.
PAARL ROCKS: Isuru Udana, Tabraiz Shamsi, Hardus Viljoen, Faf du Plessis (capt), Bjorn Fortuin, James Vince, Kyle Verryene, Cameron Delport, Henry Davids, Sibonela Makhanya, Kerwin Mungroo.