The home team scored four tries to the Lions' three but the visitors did pick up a losing bonus-point from the contest for losing by seven points.
It was the Lions that made an almost perfect start to the contest when Ruan Venter went over for a try that was converted by Chris Smith.
Smith then converted a penalty to extend the lead but the Stormers hit back as wing Dylan Maart showed his pace to score his side's first try.
The visitors took a 17-10 into the halftime break when Venter broke away from a rolling maul and Smith again slotted the conversion.
The Stormers must have had roasting in the dressing room because they came out firing after the interval with Wandisile Simelane going over for a five-pointer.
Paul de Villiers then dotted down to take the home team into the lead for the first time in the contest.
The teams exchanged penalties before the the Stormers struck again, with Evan Roos forcing his way over for the bonus-point try.
The Lions pulled one back through wing Kelly Mpeku but it proved to be a consolation as the hosts held on for the victory.
Scrumhalf Jaden Hendrikse played a crucial role in the Sharks' attritional United Rugby Championship victory over the Bulls on Saturday, earning the praise of interim coach JP Pietersen.
Stormers boss John Dobson admitted he mustn't be too critical given the Stormers are sitting pretty at the top of the United Rugby Championship table.
Lions head coach Ivan van Rooyen had plenty of silver linings to focus on despite his men going down 34-27 to the undefeated Stormers in their United Rugby Championship encounter on Saturday.
The Sharks' secured a 21-12 victory over the Bulls at a near-capacity Kings Park on Saturday, a result that further lifted the Durban side's spirits in the United Rugby Championship.
