The Bulls scored 16 unanswered points against the Stormers to record a good first victory away from home in their defence of their Rebel Sport Super 14 title at Newlands.
After struggling to come to terms with a partisan crowd and a hostile home side, the Bulls found themselves on the wrong end of referee Willie Roos' whistle as they conceded five penalties and four free-kicks in the first half hour without reply.
Three of those were converted by Stormers first five-eighths Peter Grant, who also missed two attempts at goal, but saw his side into a 9-0 lead against a Bulls side who looked to be struggling.
But a pressure try by wing Bryan Habana just before the break brought his side back into it, although they may have paid a high price.
Habana injured his shoulder in the dive and left the field at the break, returning to sit on the bench with a heavily iced shoulder under constant medical supervision.
However, in the second half both sides struggled to come to terms with the new laws of the game, and it resulted in much frustration for both teams.
The Bulls pack - led by an outstanding Wikus van Heerden - started to get the upper hand and clawed their way into the lead.
First five-eighths Derick Hougaard put over a tough sideline penalty to put the Bulls into the lead, then added two more as the pressure started to count to ensure his team couldn't lose the game.
But in the dying seconds a free-kick saw Springbok Sevens specialist Gio Aplon break through and get pulled down five metres from the line.
However, the Stormers fluffed the recycled ball to send the Bulls into celebrations.
Bulls 16 (Bryan Habana try; Derick Hougaard con, 3 pen) Stormers 9 (Peter Grant 3 pen). HT: 7-9