The home side, losing semi-finalists last season and runners-up in 2010, also scored three tries through Gio Aplon, Siya Kolisi and a penalty try to go with Pietersen's haul.
The Hurricanes saw Tim Bateman and Beauden Barrett cross for tries, while Barrett added both conversions and four penalties to match Pietersen's points haul of 21, but the visitors could not claim their first win in Cape Town since 2006 despite a brave fightback.
The Hurricanes were always up against it after falling 20-6 behind with Stormers winger Aplon opening the scoring in the sixth minute and Kolisi going over following a driving maul in the 28th minute - moments after the visitors had lost Tristan Moran to a yellow card.
Kolisi was on as a replacement for Stormers captain Schalk Burger, who went off with a knee injury in the 15th minute and was taken to hospital.
Pietersen, who is back in South Africa after a stint with French side Bayonne, converted both those tries and also added two penalties, while the Hurricanes could only get on the scoresheet through a pair of Barrett penalties in the opening half-hour.
However, the New Zealand side staged an impressive recovery as they managed to get back on level terms by the eighth minute of the second half.
They reduced the deficit to seven points at half-time at 23-16 - despite losing a second prop to the sin-bin in the 35th minute with Ben May the man to leave the fray.
A Barrett penalty and a Gary van Aswegen drop-goal kept the Stormers 14 points ahead at 23-9, but the Hurricanes hit back just before the interval when Bateman raced away for a try that was converted by fly-half Barrett
The Hurricanes were still a man down as the second half started but, after Pietersen missed a shot at goal, they levelled the scores up at 23-23 when Barrett scored an intercept try that also saw him add the extra points.
That was as good as it got for the Hurricanes, though, as the Stormers gradually eased clear over the final half-hour to take the win.
Pietersen fired over three penalties and also hit the post with another with the Hurricanes only being able to respond with another Barrett three-pointer.
The Stormers then assured themselves of the win in the 72nd minute when they were awarded a penalty try in an incident that saw Hurricanes replacement Jeffery Toomaga-Allen become his side's third prop to be shown a yellow card.
Full-back Pietersen added the conversion to complete the scoring, although he saw a late try disallowed that would have earned his side a bonus point.