A dominant first-half show from the Lions was enough to secure a comfortable victory over their South African rivals.
The Lions led 24-6 at half-time but the Stormers fought back to salvage a losing bonus point.
The Lions went ahead when, after attacking from a lineout in the Stormers half, centre Henco van Wyk broke through to the 5m line where full-back Warrick Gelant impeded at the breakdown, earning a yellow card and Gianni Lombard kicked a penalty.
Jurie Mathee hit back with a penalty but Morne van den Berg went over for the opening try before Henco van Wyk and Marius Low joined him ove...