The Capetonians were leading 10-0 at the halfway stage through a converted try and a penalty goal. They added three more converted tries and another penalty goal after the break, with Irish responding twice in an entertaining second half.
London Irish were looking for their first win of this year’s campaign as they travelled to South Africa to take on the Vodacom United Rugby Championship winners on their home turf.
Last weekend Irish fell 32-27 at home to Montpellier in the first round, while the DHL Stormers chased their maiden victory in the competition after they lost 24-14 at Clermont in France.
The Cape side may have let an 11-point lead slip at Stade Marcel-Michelin, but they again showed why they are a very different prospect at home, having won all 15 of their previous home fixtures in all competitions.
Lovely soft hands from Springbok prop Steven Kitshoff released flanker Willie Engelbrecht, who powered over from close range for the opening try which was converted by Manie Libbok.
However, the team in blue and white thought they might have doubled the lead through Springbok lock Salmaan Moerat who finished off a brilliant counter-attack which started inside their own half. But the jubilation of the home crowd was short-lived as the brilliant effort was ruled out through a forward pass in the build-up.
Speedy wing Angelo Davids was also twice denied through rock steady tackling, while the team was otherwise rewarded when the dependable Libbok steered an easy penalty goal through the uprights to take the halftime score to 10-0.
Impressive No 8 Hacjivah Dayimani got the home side off to a flying start when he ran in their second try from a Damian Willemse offload. Libbok was accurate off the tee with his conversion as he raised the flags to take the score to 17-0 with still plenty of rugby left to be played.
The livewire No 8 then initiated another superb DHL Stormers try dotted down by the free-scoring Leolin Zas, and with Libbok making no mistake with the extras, the Cape side were now comfortably ahead by 24 points.
But Irish hit back with their first try from a powerful lineout maul, with former DHL Stormers hooker Mike Willemse dotting down for the try converted by Paddy Jackson.
Libbok showed his accuracy once more off the tee when he succeed with a penalty goal to take the score to 27-7 with just under 20 minutes to go in this absorbing encounter.
Replacement back Ben White then thought he ran in for the visitors' second try, however, this effort was ruled out too because of a knock-on as a result of Davids' try-saving tackle.
Another visiting replacement, English international Will Joseph, waltzed his way through the home defence to score under the posts and with Jackson adding the easy extras, Irish reduced the gap to 27-14 with only five minutes of play remaining. Joseph was also called back moments later when he also thought he scored again, but the try was ruled of because of an infringement.
To the absolute joy of the home supporters, replacement loose forward Junior Pokomela added a fourth try - for a bonus point - after normal playing time was up to make the final score 34-14 for a splendid home win for the Cape side.
DHL Stormers 34 (10) - Tries: Willie Engelbrecht, Hacjivah Dayimani, Leolin Zas, Junior Pokomela. Conversions: Manie Libbok (4). Penalty goals: Libbok (2).
London Irish 14 (0) - Tries: Mike Willemse, Will Joseph. Conversions: Paddy Jackson (2).