The Cape Town-based Stormers nosed in front through a 64th minute try by winger Gio Aplon and grimly defended the slender lead for the remaining minutes on a gusty evening.
Hurricanes fly-half Beauden Barrett set up the Hurricanes' first try on the stroke of half-time, but cost his team a near-certain try with 10 minutes left to play with a pass that failed to find one of his team-mates who were streaming towards the line.
Coming off a bye after an indifferent start to the season that has yielded only three wins, the Stormers face another three matches of a gruelling four-match tour of New Zealand and Australia, but will be galvanised by an even performance across the team at FMG Stadium.
The Hurricanes, who notched their fourth loss midway through the southern hemisphere competition, dominated possession early but went a man down in the 28th minute when lock Jeremy Thrush was sin binned for deliberately bringing down a rolling maul near the try-line.
The Stormers unleashed another powerful maul a few minutes later and barged 10 metres over the line to secure their first try through flanker Michael Rhodes.
The Hurricanes' classy backline wrenched back the momentum at the end of a sustained burst in the final minutes of the half, with winger Matt Proctor gliding over at the left corner after a pinpoint pass from Barrett.
South Africa winger Bryan Habana, returning to the side after a long layoff with a knee injury, brilliantly charged down Barrett's conversion kick after the siren to limit the deficit to 11-7 at half-time.
Pietersen slotted two penalty goals to put the Stormers two points up 14 minutes after the break, but the Hurricanes responded with a brilliant team try on the hour mark.
Flanker Brad Shields made a dart toward the line, spun around in a tackle and offloaded to fullback Andre Taylor who dived over at the right corner for the Hurricanes' second.
The Stormers made a stunning response four minutes later, with barnstorming number eight Duane Vermeulen crashing toward the line and Gio Aplon ghosting through the Hurricanes' defence to collect a sharp pass and roll over the line under a pile of players.
The Hurricanes blew a gilt-edged chance to recapture the lead with 10 minutes left, when Barrett hurled a long pass to the left corner that proved too hot for streaming winger Proctor to handle.
The ball spilled over the touchline to the Stormers' relief and the Cape Town side defended stoutly to secure a morale-boosting win.