In a tryless encounter, the Stormers emerged victorious as three penalties from Joe Pietersen and two more from replacement Peter Grant cancelled out the four penalties slotted over by Sharks fly-half Patrick Lambie.
Grant fired over the winning penalty three minutes from time at Newlands.
The result sees 2010 runners-up the Stormers join the Bulls, Reds and Highlanders with 100% records after two rounds, while the Sharks are still looking for their first win.
In a match littered with penalty opportunities for both teams, the Sharks had the first chance to draw blood in the eighth minute but Lambie missed his three-point attempt.
However, after sustained pressure from the visitors, Lambie was handed another chance in the 10th minute and he took advantage to make it 3-0.
That lead did not last long though, and within seven minutes the Stormers were 6-3 ahead on the back of two Pietersen penalties.
Lambie made it 6-6 in the 21st minute but he then missed another penalty attempt eight minutes later from halfway before Sharks full-back Riaan Viljoen failed with a drop-goal attempt.
Lambie also missed a drop-goal in the 37th minute, but with the advantage going to the Sharks, play was pulled back for a penalty to the visiting side, which Lambie slotted over to give his team a 9-6 half-time lead.
It was a similar story in the second half, with penalties proving the only way of scoring.
Pietersen, who kicked 21 points in last weekend's 39-26 home win over the Hurricanes, missed two chances to make it 9-9 within five minutes of the restart but he made no mistake in the 54th minute to level up the scores.
By that stage Grant was on the pitch and, after Pietersen missed another chance in the 56th minute, the South Africa international fly-half took over the duties and he put the Stormers into the lead with his opening opportunity on the hour mark.
That penalty came following an infringement that saw Sharks forward Ross Skeate sin-binned.
Pietersen spurned another penalty to put the Stormers further ahead in the 71st minute and it looked as though the Sharks might claim a share of the spoils when Lambie slotted over his fourth kick of the match to make it 12-12 with time running out.
However, it would be the Stormers celebrating at the end as Grant successfully converted his 77th-minute effort to give his side the win in Cape Town.