The men from Kimberley sealed the victory through an 82nd-minute try from close range by replacement flank Carel Greeff and right wing Nico Scheepers' conversion.
The victory was nothing more than Griquas deserved as they outplayed the Sharks in the set-pieces, especially the scrums.
Springbok hopeful Lourens Adriaanse led the way, and at the breakdowns, where the home side suffered from a lack of accuracy and discipline.
Griquas had raced into a 13-0 lead after 15 minutes, but trailed 16-20 at the break.
They were denied a try early in the second half when the TMO controversially ruled there had been an obstruction in the build-up after protests from the Sharks players.
Neither side showed much inclination to run the ball in overcast, windy conditions that turned to rain in the second half.
Griquas scored the first try in the fourth minute as flank Marnus Schoeman went over after a lineout near to the Sharks' line.
Scheepers converted and then added two penalties to set the tone for what would be a top-class kicking display by the 23-year-old, who succeeded with all eight of his shots at goal.
A brace of penalties by Sharks flyhalf Butch James cut the deficit to 6-13 midway through the first half.
Last year's beaten finalists scored their first try on the half-hour after a controversial decision by referee Jason Jaftha.
A big scrum from Griquas saw them marching forward on their own ball, but Jaftha penalised them.
Sharks scrumhalf Charl McLeod took a quick tap and made plenty of ground before captain and No 8 Jacques Botes picked up the ball and dived over the tryline.
The conversion by James levelled the scores, but a penalty by Scheepers just two minutes later restored a 16-13 lead for Griquas.
Botes, who stood in for regular skipper Keegan Daniel, went over for his second try on the stroke of half-time as he jinxed through the defensive line off a retreating scrum, with James converting.
Centre Howard Mnisi, the pick of all the backline players on display, earned Scheepers another penalty after cruising through a gap on a lovely break.
The ill-discipline of the Sharks at the rucks gave Scheepers two further penalties in the second half, either side of the Sharks' third try.
Sharks wing Lwazi Mvovo's 66th-minute try came after a clearing kick by Griquas flyhalf Francois Brummer had been half-charged-down and fell into the hands of replacement scrumhalf Cobus Reinach.
Fullback Odwa Ndungane then exploded down the left touchline before passing inside for Mvovo to trot over for the try and a 27-22 lead for the Sharks.
Scheepers added his sixth penalty in the 74th minute to close the gap to 25-27, but James converted a penalty three minutes later to restore their two-point lead.
Nothing short of a try would then suffice for Griquas and a series of pick-and-goes saw them camped on the Sharks line after the hooter went. A powerful drive by Greeff then saw him over the line for a try confirmed by the TMO.
Scheepers was left with a conversion 20m in from touch and he sealed a wonderful victory for the Currie Cup underdogs.
Sharks:
Tries: Jacques Botes (2), Lwazi Mvovo
Conversions: Butch James (3)
Penalties: James (3)
Griquas:
Tries: Marnus Schoeman, Carel Greeff
Covnerison: Nico Scheepers (2)
Penalties: Scheepers (6)
Teams:
Sharks:
15. Odwa Ndungane, 14. Sizo Maseko, 13. Louis Ludik, 12. Tim Whitehead, 11. Lwazi Mvovo, 10. Butch James, 9. Charl McLeod, 8. Jacques Botes (captain), 7. Jean Deysel, 6. Brynard Stander, 5. Marco Wentzel, 4. Edwin Hewitt, 3. Wiehahn Herbst, 2. Kyle Cooper, 1. Dale Chadwick
Substitutes: 16. Craig Burden, 17. Rayno Gerber, 18. Peet Marais, 19. Tera Mtembu, 20. Cobus Reinach, 21. Fred Zeilinga, 22. Jaco van Tonder
Griquas:
15 Gouws Prinsloo, 14 Nico Scheepers, 13 JP Nel, 12 Howard Mnisi, 11 PJ Vermeulen, 10 Francois Brummer, 9 Jacques Coetzee, 8 Burger Schoeman, 7 Jaco Nepgen, 6 Marnus Schoeman, 5 Ligtoring Landman, 4 Hilton Lobberts, 3 Lourens Adriaanse, 2 Ryno Barnes (captain), 1 Steph Roberts
Substitutes: 16 Matt Dobson, 17 Nick Schonert, 18 Jonathan Adendorf, 19 Carel Greeff, 20 Marnus Hugo, 21 Du Randt Gerber, 22 Rocco Jansen