The Bulls snapped a four-game losing streak as Strauss led from the front in what was a South African record 149th appearance in the Southern Hemisphere club championship for the former Springboks captain.
Winger John-Ben Kotze and centre Jesse Kriel also crossed the line for the home side, while the Stormers, who played for 20 minutes with 14 players, scored through lock Jan de Klerk, centre Damian de Allende and flank Siya Kolisi.
"We are glad to get back to winning ways. Adriaan getting the record and getting a win for him is special," Bulls captain Burger Odendaal said at the post-match presentation.
"We really focussed hard on getting our defensive line high on to them. There were still a lot of mistakes, but we are improving."
Strauss powered over for his first try inside the opening five minutes as the Bulls got a big shove going after a line-out.
The visitors replied with a penalty from flyhalf Damian Willemse, but suffered a set-back when centre De Allende received a yellow card for repeated infringements.
A minute later Strauss crossed over again as the Bulls pack showed their muscle once more and Kotze crossed after being fed by Warrick Gelant.
But two tries before halftime brought the Stormers roaring back into the contest.
De Klerk dived over the line from close-range, before De Allende created a piece of magic as he collected his own chip ahead to narrow the Bulls' lead to 19-18 at the break.
The Stormers’ discipline proved their downfall again though when Pieter-Steph du Toit was sent to the sin-bin for an infringement at the maul and his team lost a line-out on their own throw as the ball went straight to Strauss, who ran over the line unopposed.
Kolisi reduced the deficit to three points with a try in the corner, but the Bulls hit straight back as Kriel profited from Kotze’s offload to score.
"Every time we got the momentum we made a mistake and losing two players made it even tougher. Not getting out of our own half was a big mistake through the game from us," Kolisi said.
(Reporting by Nick Said, editing by Ed Osmond)
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