Leinster lost for the second time in three Guinness Pro12 outings as they went down 10 points to 9 at the Sportsground.
The Blues raced out of the starting blocks and built up a 9 point lead through three Ian Madigan penalties.
Jack Carty chipped away at that lead with a penalty and he split the posts with the winning converson after scrum half Kieran Marmion had touched down for a brilliant individual try.
