Peter Grant's boot did the damage as Stormers edged out Super Rugby opponents Cheetahs 16-14 despite being outscored by two tries to one.
Stormers, who lie second a point behind Bulls in the South African conference, scored all their points in the first 24 minutes and then had to watch Cheetahs chip away at their total before ultimately falling short.
Grant scored three penalties and converted Eben Etzebeth's 22nd-minute try to give the home side the advantage before Cheetahs' second-half resurgence.
They touched down twice through Hennie Daniller and Willie Le Roux, with substitute Riaan Smit adding both conversions.
Grant scored from the first penalty of the match after 10 minutes and made it 6-0 when he sent another through the posts three minutes later.
After 17 minutes Grant had his third successful kick following Heinrich Broussow's infringement.
Stormers put together the first try-scoring move of the game five minutes later, Etzebeth finishing from close range and Grant slotting the extras, as the lead reached 16-0.
Grant hit the upright with a long penalty but there was no further scoring before the break.
Cheetahs hit back when Le Roux set up Daniller for a 47th-minute score, with Smit making it a seven pointer.
Rynardt Elstadt was sin-binned after 55 minutes to hand the visitors a numerical advantage which they failed to convert into points.
A Le Roux interception try and another conversion from Smit set up a tense last 12 minutes but Stormers held on to their two-point advantage.