Bulls replacement flyhalf Tian Schoeman had kicked a 51-metre effort to level the scores two minutes from full-time, but the hosts' hopes of claiming a draw looked forlorn as Pietersen lined up what would have been a winning penalty.
The Sharks players were celebrating as if they had won the match but Pietersen's effort was off target leaving everyone inside the Loftus Versfeld stadium stunned.
The Bulls' points came via a try from fullback Warrick Gelant, while starting flyhalf Francois Brummer kicked a penalty, conversion and drop-goal, but also missed three kickable efforts.
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The Sharks came from behind in the second half as fullback Willie le Roux got their only try, and Pietersen kicked a conversion and three penalties, before fluffing his easiest opportunity of the night at the death.
The Bulls are the only team in the competition who have yet to concede a first-half try this season and kept the Sharks at bay again in the opening 40 minutes.
The only try of the first period was scored by the Bulls' Gelant, who stepped past two defenders and touched down to give his team a 13-6 halftime lead.
The visitors levelled the scores 10 minutes into the second period with a try from Le Roux, who chased his own kick behind the Bulls' defensive line and crossed over following a fumble from Gelant.
The Sharks were ahead for the first time in the game shortly afterwards when Pietersen landed his third penalty after the Bulls were penalised for an infringement at the breakdown.
Le Roux might have extended that lead minutes later when he had a chance to score in the corner but elected to pass rather than go for the line himself and the ball was knocked on.
He was made to pay as Schoeman kicked a long-range penalty to level the scores at 16-16.
(Reporting By Nick Said; editing by Toby Davis)
