A try in each half gave Leinster their first Celtic League win on Welsh soil this season and ended Cardiff Blues' unbeaten home record.
Cardiff (3) 6:
Pens: L Thomas (2)
Leinster (10) 15:
Tries: Quinlan, Dempsey
Centre David Quinlan scored the first after just 39 seconds when he collected Felipe Contepomi's chip kick.
Contepomi added a penalty before the Blues fought back with two penalties from young fly-half Lee Thomas.
The home side pressed throughout the second-half but Girvan Dempsey dealt the killer blow five minutes from time.
Leinster's opening try came in their first attack as they cut though the home side's defence with alarming ease.
Fly-half Contepomi breezed past the would-be tacklers, chipped over the full-back and Quinlan was on his shoulder to collect the loose ball and force his way over at the foot of the posts.
Contepomi added the conversion for a seven-point lead with less than two minutes on the clock.
He added another three points from a penalty on 25 minutes before Thomas slotted over his first penalty attempt to get the Blues on the scoreboard.
Martyn Williams almost crossed for the Blues in first-half injury time, but his 30-yard break from an over-thrown Leinster line-out was ended by a desperate ankle tap with the tryline in sight.
Thomas' second penalty cut the gap to just four points early in the second half, and the home side began to dictate the game.
The Blues' hopes were not helped as first Tom Shanklin and then Thomas departed with injuries - adding to the Cardiff region's already crippling casualty list - but the Irish province looked there for the taking as they tired in the closing stages.
But a touch of class from replacement Gordon Darcy secured the win for Leinster.
Darcy collected a loose kick 10 metres inside his own half, brushed off the first tackler and sprinted on the outside into Blues territory before giving a perfectly reverse pass to the on-rushing Dempsey.
Blues: M Nuthall; D Dewdney, T Shanklin, J Bryant, C Morgan; L Thomas, R Powell; J Yapp, G Williams, G Jenkins, D Jones, R Sidoli, K Schubert, M Williams (capt), J Malpas.
Replacements: B Evans, R Thomas, J Goode, R Sowden-Taylor, N Macleod, T Davies, S James.
Leinster: G Dempsey, J McWeeney, K Lewis, D Quinlan, G Brown; F Contepomi, G Easterby; E Byrne, S Byrne, R Nebbett, M O'Kelly, B Gissing, A McCullen, S Jennings, E Miller.
Replacements: J Lyne, G Hickie, C Potts, V Costello, B O'Meara, D Holwell, G D'Arcy.
Referee: Malcolm Changleng (Scotland)