The Stormers won their first match of the season and also handed the defending champion Chiefs their first defeat of 2013.
Despite outscoring the Stormers by four tries to three - which handed the visitors two bonus points - the home team relied on the boot of Joe Pietersen and their famous defence to win the day.
The Stormers got off to a flying start - a Joe Pietersen penalty and Gio Aplon try giving them a 10-0 lead after just eight minutes.
But the Chiefs showed just how dangerous they can be when a team just slightly drop its intensity, a Charlie Ngatai try coming after an error by the home team. The conversion and earlier penalty by Gareth Anscombe suddenly had the Stormers leading by just three, 13-10 - after Pietersen had kicked a second penalty between the two Chiefs scores.
Pietersen took the lead back out to six points with his third penalty, before Tawera Kerr-Barlow was yellow carded for repeated infringements at the breakdown by the Chiefs. Pietersen slotted the penalty to make it 19-10 just after the half-hour mark.
Despite being a man down and Cruden playing at scrumhalf, the Chiefs scored the next - a brilliant try, with Tim Nanai-Williams collecting a Cruden grubber. Anscombe added the extras to make it 17-19.
However, when Rynhardt Elstadt managed to dislodge the ball in a tackle from the restart, and then hack it ahead, Aplon followed up to collect and score his second of the match. Pietersen's conversion made it 26-17 - which was also the half-time score.
Anscombe pulled three points back six minutes into the second half, as the Chiefs started to make use of the wind that was now at their backs.
However, it was Nic Groom who got the next score, as the Stormers produced a sublime moment of magic - using the ball off the back of the line-out with a number of phases and Groom going over. Pietersen's conversion made it 33-20, leaving the visitors with a mountain to climb.
And they started that climb very quickly, the Chiefs' outside backs showing just how dangerous they can be to put Charlie Ngatai over for his second try. Anscombe's conversion made it 27-33, with the final quarter approaching.
A Pietersen penalty soon afterwards gave the Stormers some breathing space at 36-27, before some phenomenal hands from the Chiefs put Andrew Horrell away in the corner for a great try. Anscombe's conversion ensured the Stormers were made to defend like demons for the last five minutes.
The Chiefs had their chances, but another yellow card - with Nick Crosswell sent to the sin bin for repeated infringements at the tackle - allowed home team to hang on for a vital win.
For the Stormers:
Tries: Aplon 2, Groom
Cons: Pietersen 3
Pens: Pietersen 5
For the Chiefs:
Tries: Ngatai 2, Nanai-Williams, Horrell
Cons: Anscombe 4
Pens: Anscombe 2
Yellow cards: Tawera Kerr-Barlow (Chiefs, 32 - repeated infringements at the breakdown), Nick Crosswell (Chiefs, 74 - repeated infringements at the tackle)
Stormers: 15 Joe Pietersen, 14 Gio Aplon, 13 Jean de Villiers (captain), 12 Damian de Allende, 11 Bryan Habana, 10 Elton Jantjies, 9 Nic Groom, 8 Duane Vermeulen, 7 Rynhardt Elstadt, 6 Siya Kolisi, 5 Andries Bekker, 4 De Kock Steenkamp, 3 Frans Malherbe, 2 Deon Fourie, 1 Steven Kitshoff.
Replacements: 16 Tiaan Liebenberg, 17 Pat Cilliers, 18 Don Armand, 19 Nizaam Carr, 20 Dewaldt Duvenage, 21 Peter Grant, 22 Gerhard van den Heever.
Chiefs: 15 Gareth Anscombe, 14 Lelia Masaga, 13 Tim Nanai-Williams, 12 Charlie Ngatai, 11 Asaeli Tikoirotuma, 10 Aaron Cruden, 9 Tawera Kerr-Barlow, 8 Liam Messam, 7 Sam Cane, 6 Tanerau Latimer, 5 Brodie Retallick, 4 Craig Clarke (captain), 3 Ben Afeaki, 2 Mahonri Schwalger, 1 Pauliasi Manu.
Replacements: 16 Hika Elliot, 17 Ben Tameifuna, 18 Michael Fitzgerald, 19 Nick Crosswell, 20 Augustine Pulu, 21 Andrew Horrell, 22 Patrick Osborne.
Referee: Jaco Peyper (South Africa)
Assistant referees: Jonathan Kaplan (South Africa), Ben Crouse (South Africa)
TMO: Deon van Blommestein (South Africa)