Two Halfpenny penalties and a Gethin Jenkins try brought the Blues back into the contest.
But with the stage set for a crucial scalp for the Welsh region Welsh international full-back Halfpenny crucially missed two penalties in quick succession just after the hour mark.
With just a point between the sides Leinster's Fergus McFadden then kicked Joe Schmidt's side past the winning post with a penalty 13 minutes from time.
The Blues, who had Gavin Henson withdraw before kick-off with a calf injury, went behind in the fifth minute when No. 8 Jamie Heaslip fed O'Brien to crash under the posts.
Fly-half Jonathan Sexton added the extras before Kearney went over for his side's second try three minutes later - Sexton again kicking the conversion for a 14-0 lead.
Welsh international Halfpenny began the fight back on 17 minutes when he booted his first penalty, and followed that up three minutes later with another.
Fly-half Dan Parks - retained in Andy Robinson's Scotland Six Nations squad despite suggestions otherwise - then got in on the act with a drop-goal before Sexton's three-pointer just before the break sent Leinster in 17-9 ahead.
Halfpenny's third penalty of the contest 11 minutes after the restart seemed to galvanize the Blues, as prop Jenkins then barged over from close-range to reduce the deficit still further.
The full-back's subsequent conversion brought the Blues to within one point. However the wheels then fell off for the 23-year-old as he missed two glorious opportunities to snatch the game.
His 63rd minute penalty fell short, and he then screwed another wide two minutes later as the chance of a remarkable comeback slipped away with it.
Outside centre McFadden then showed him how to do it as he extended Leinster's winning league run to ten games.
|Cardiff Blues Score Card|
|Leinster Rugby Score Card|