The Cape Town-based Stormers overpowered the Pretoria-based Bulls 29-17 in their north-south South African derby, also the 100th Super Rugby appearance for Stormers captain Siya Kolisi.
The Stormers and coach Robbie Fleck have been under pressure after many poor performances this season.
They needed a big performance in front of a good crowd, starting strongly and maintaining that through the match.
John Mitchell, by contrast, has had no such problems. His young Bulls team have been impressing with some mature displays and big wins against teams that were thought too strong for them.
In a game centred on the battle between two bruising sets of forwards, the Stormers pushed 12-0 ahead in the first 11 minutes, prompting a response from the Bulls big men.