The Sharks responded with two tries to regain control, but Leinster had the final say when Andrew Osborne touched down a Prendergast kick late on.
Leinster have suffered a second straight defeat in the URC, going down 26-20 to the Sharks in Durban.
The defending champions trailed 14-7 at half-time before fighting back after the break, with Kildare's Sam Prendergast kicking a penalty that briefly put Leinster in front.
The Sharks responded with two tries to regain control, but Leinster had the final say when Andrew Osborne touched down a Prendergast kick late on.
That score secured a losing bonus point for Leinster, but they remain without a win after the opening two rounds.

Power Fires Seven-Under 64 To Climb Leaderboard In Utah
Ireland Run In Seven Tries To Complete Double Over Japan
Sunday Morning Sports Update
SFC/IFC/JFC Results & Sunday Fixtures
Galway's Liam Nolan Claims First Professional Title In Abu Dhabi
FAI Rejects Racism Allegation As Ireland-Israel Press Conference Ends Abruptly
Meadow Makes Cut As Maguire And Kildare's Walsh Miss Out In Hawaii
Luke Humphries Through To World Grand Prix Semi-Finals After 3-0 Win