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.
Towering lock Lood de Jager and flanker Jason Jenkins went in between the posts to turn it around at 17-12 to the Bulls early in the second.
The Bulls' only lead of the game lasted two minutes as Stormers centre Damian de Allende set up a try for fullback SP Marais with a break down the short side. The Stormers pulled away in the last half-hour with a fourth try to hooker Ramone Samuels, who made up for his earlier sin-binning for a late tackle.