AS IT HAPPENED: Sharks v Stormers
The hosts had led throughout the game and scored the only try through scrumhalf Cobus Reinach on the stroke of half-time.
But Frans Steyn missed two crucial penalties when the lead was brought down to a single point just after the hour and Taute capitalised on the final whistle.
The result means that the Sharks' lead at the top of the Overall log is now just two points with two games to play, while the Waratahs and Crusaders behind them have a game in hand.
They had started out the contest brightly and were ahead after only three minutes when Juan de Jongh was penalised for side entry, allowing Steyn to punt over his first points.
There was a second penalty the Sharks flyhalf landed after 10 minutes, which came at a cost too, as Nizaam Carr was sent to the sin bin following a reckless high tackle on Reinach.
The Sharks failed to capitalise further on their man advantage, though, and even conceded three points when S'bura Sithole failed to clear out the way of a high ball and was called for obstruction by referee Jaco Peyper - Kurt Coleman, who kicked 12 points, hitting the target with his first shot at goal.
When Carr returned, the visitors grew even stronger, and when Etienne Oosthuizen was tackling illegally, the Stormers' number 10 made it 6-6 after 25 minutes.
However, Steyn booted the home side back in front when Pat Cilliers strayed off-side.
But again the Capetonians hit back following off-sides against Oosthuizen and Reinach as they strayed off-side.
The first try eventually arrived two minutes before the break when Sithole showed good pace as he stepped inside his man with Reinach picking up the pieces and darting over for his fifth try of the campaign.
The seven point half-time lead was slashed to four within five minutes of the restart as Oosthuizen conceded his third penalty - this one for an infringement at the breakdown - and Coleman did the rest.
An accidental off-side by Sailosi Tagicakibau allowed the Sharks to regain their lead, but again the Stormers hit back after a dangerous tackle by Reinach on Cheslin Kolbe, with the subsequent penalty converted by replacement flyhalf Demetri Catrakilis.
Coetzee was sent to the sin-bin for more illegal play as Catrakilis made it a one-point game.
Steyn could have gained back some breathing space with 11 minutes to play, only to miss his first kick of the night when Alistair Vermaak was punished for side entry into a ruck.
He missed another, striking the crossbar, with four minutes to play, before Taute landed his drop kick to massive celebrations from the visitors.
Super Rugby now breaks for the Incoming Series matches, but when it does resume, the Stormers' next match will be against the Bulls in Cape Town (Saturday, July 5 at 17:05) while the Sharks travel to Bloemfontein to face the Cheetahs (Saturday, July 5 at 19:10).
Scorers:
Sharks
Try: Cobus Reinach
Conversion: Frans Steyn
Penalties: Steyn (4)
Stormers
Penalties: Kurt Coleman (4), Demetri Catrakilis (2)
Drop goal: Jaco Taute
Sharks
15. SP Marais, 14. JP Pietersen, 13. S’bura Sithole, 12. Paul Jordaan, 11. Lwazi Mvovo, 10. Francois Steyn, 9. Cobus Reinach, 8. Willem Alberts, 7. Tera Mtembu, 6. Marcell Coetzee, 5. Stephan Lewies, 4. Etienne Oosthuizen, 3. Jannie du Plessis, 2. Bismarck du Plessis (captain), 1. Tendai Mtawarira
Substitutes: 16. Kyle Cooper, 17. Dale Chadwick, 18. Lourens Adriaanse, 19. Ryan Kankowski, 20. Keegan Daniel, 21. Charl McLeod, 22. Tim Swiel, 23. Heimar Williams
Stormers
15. Jaco Taute, 14. Cheslin Kolbe, 13. Juan de Jongh, 12. Damian de Allende, 11. Sailosi Tagicakibau, 10. Kurt Coleman, 9. Nic Groom, 8. Duane Vermeulen (captain), 7. Siya Kolisi, 6. Nizaam Carr, 5. Ruan Botha, 4. Michael Rhodes, 3. Pat Cilliers, 2. Stephan Coetzee, 1. Alistair Vermaak
Substitutes: 16. Mike Willemse, 17. Sti Sithole, 18. Martin Dreyer, 19. Jean Kleyn, 20. Manuel Carizza, 21. Dylon Frylinck, 22. Demetri Catrakilis, 23. Peter Grant