Dickinson and Taylor had been early first half try scorers before Kieran Lewis punished slack Edinburgh defending to dart over with David Holwell converting. However Edinburgh bounced back and had the bonus point before the interval.
Derrick Lee completed a slick passing move to score in the corner before Phil Godman's touchdown, converted by Laney, gave Todd Blackadder's men a 17-point cushion.
But Guy Easterby handed Leinster a lifeline on the stroke of half-time when he punished poor defending to nip in under the posts to give Holwell an easy conversion and the Irish added a third score just after the break when Christian Warner outpaced the home defence to touchdown Holwell's chip kick.
However with the gap down to five points Marcus Di Rollo calmed Edinburgh nerves when he sprinted home from halfway for a vital interception try.
Simon Webster then boosted his hopes of a Scotland call-up with a sizzling score in the corner after a sweeping move by the Murrayfield men. Dickinson doubled his tally moments later before Warner added his own second, converted by Holwell.
Holwell then set up a jittery conclusion for the Gunners by converting his own try with six minutes remaining but the home side withstood fierce Irish pressure.
|Edinburgh Rugby Score Card|
|Marcus di Rollo||1||5|
|Leinster Rugby Score Card|