The Stormers led 6-3 midway through the first period after two penalties by Kurt Coleman and a solitary reply from Nicolas Sanchez before the home flyhalf was sent to the sinbin for the second time in three games.
The visitors, already camped on the Jaguares line, made the most of their extra man to notch the first try as fullback Cheslin Kolbe sidestepped three defenders before going over.
With Coleman's conversion, the Stormers opened a 10-point lead but the Argentine team cut that back to five with a try in added time, the returning Sanchez making a break and centre Jeronimo de la Fuente touching down.
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Jaguares let themselves down in the opening half hour with handling errors that prevented them from building the same penetrative attacking runs that thrilled their fans in a 30-26 defeat against the Chiefs last weekend.
The hosts charged down to the Stormers end from the restart following a break by lock Tomas Lavanini who fed Tomas Lezana but the young flanker dropped the ball as he was going over the line.
The Jaguares continued to take the game to the Stormers and won a penalty. The normally reliable Sanchez missed his second kick of the match and replacement flyhalf Santiago Gonzalez also failed to score with an effort from the halfway line.
The Argentines, who suffered a third successive defeat, would not have been flattered if they had snatched victory but the Stormers underlined their experience and pragmatism by holding on for the win.
(Editing by Tony Jimenez)
