The Cheetahs outscored the Stormers by five tries to three for only their second win of the season, with Brussow named Man-of-the-Match for the massive role he played.
“It was a real team effort but Heinz (Brussow) made a big impact. We really look up to him, and the youngsters in the side also stood up for us,” said Strauss.
The Stormers conceded their most tries in a local derby since the Sharks and Bulls put five and seven respectively past them in 2007.
“I think it was important for us to build more phases, be more patient and respect the ball a bit more,” Strauss said.
“It paid dividends but you also have to play cleverly against the Stormers.”
The visitors were first out of the blocks, running up a 10-0 lead after flank Nizaam Carr crashed over under the posts past a wrong-footed Brussow.
But the Cheetahs then took over and scored three great first-half tries, courtesy of Hennie Daniller, Rayno Benjamin and Willie le Roux, to go into the break with a 20-10 advantage.
The Stormers narrowed the gap to 23-15 when wing Devon Williams rounded off, before Brussow knocked a ball back for Cheetahs wing Cornal Hendricks to outstrip Williams.
And four minutes later, when prop Trevor Nyakane crashed over to increase the lead to 35-15, his joyful war dance with wing Raymond Rhule was fitting.
The Capetonians scored a late consolation try by captain Jean de Villiers, but they left the Free State without a single point, lying stranded at the bottom of the standings.