Leinster had lost 42-12 on their last visit to the same stadium in April 2024 and were shorn of their British and Irish Lions contingent for this encounter.
The hosts, themselves, were without Springboks stars Damian Willemse, Manie Libbok and Sacha Feinberg-Mngomezulu, who are on Rugby Championship duty.
But they dominated territory and possession in the first half and showed plenty of attacking flair, but led by just six points at the break through a combination of stout Leinster defence and errors and a lack of composure as they bore down on the line.
Matthee landed a sixth-minute penalty after a scrum infringement but was then off target with two further kicks at goal.
The Stormers fly-half also skewed a drop goal attempt wide as Leinster tried to keep the hosts at bay.
On 24 minutes Paul de Villiers went over from a rolling maul after a line-out, but after consulting with the Television Match Official (TMO) referee Gianluca Gnecchi disallowed the score for obstruction at the maul by Adre Smith.
Matthee’s second penalty after 32 minutes made it 6-0 after James Culhane was penalised for not releasing.
Another flowing move by the Stormers saw wing Seabelo Senatla dive over in the corner, but the score was ruled out for a forward pass in the build-up.
Matthee split the posts with another penalty two minutes into the second half and soon after scrum-half Ungerer barged over for the first try.
Sam Prendergast’s crossfield kick was tipped by a Stormers hand and the ball fell to Senatla, who made good ground and offloaded to Ungerer, who showed strength to carry two Leinster players over with him.
The TMO confirmed the ball had been grounded and Matthee added the conversion.
The Stormers number 10 added a further penalty and debutant Roos touched down following a maul from a line-out in the 62nd minute as his side cashed in on their superiority. Matthee again kicked the extras.
That score came immediately after Max Deegan had been sent to the sin-bin after a beleaguered Leinster had conceded two penalties in quick succession in their 22.
Five minutes later, Tommy O’Brien joined him on the sidelines for a head-high tackle on Senatla, reducing Leo Cullen’s side to 13 men.
Ackermann crossed for his team’s third try after the tried and tested maul procedure was executed again, Matthee contributing the additional two points to put 30 between the sides.
The bonus-point score was not long in coming as Matthee burst through for try number four and, ultimately, Leinster were relieved to hear the final whistle.