For it was tries from Sexton, the impressive Gordon D'Arcy and replacement Ian Madigan, as well as a penalty try, handed Leinster the five points and moved Joe Schmidt's side up to third.
There was little to choose between the two sides in the opening exchanges as Edinburgh, who had lost their last four in all competitions prior to kick-off, sought to avenge their 22-16 defeat in September.
After a tense opening that saw some resolute Edinburgh defence, it was the hosts who drew first blood as they won a penalty from a Leinster scrum and Greig Laidlaw made no mistake from in front of the posts on 18 minutes.
The European champions didn't take long to hit back however and Sexton had his first points of the night on 20 minutes.
An absorbing contest saw both teams enjoy plenty of possession but errors crept in when it matter and on 34 minutes came the decisive moment of the match.
With the Leinster forwards sniffing blood and mauling five metres from the line a penalty try was awarded and David Denton was sent to the sin bin, leaving Edinburgh desperate for the half-time whistle.
But after Sexton added the extras, Leinster came right back at Edinburgh and crossed the try-line again just four minutes later after a patient build-up, Sexton again converting to hand the visitors a commanding 17-3 lead.
To their credit, Edinburgh didn't capitulate and managed to scramble a penalty just before the half-time break, which Laidlaw duly knocked over, giving the hosts hope at 17-6 down at the interval.
Edinburgh stabilised after the break and kept Leinster at bay until Denton returned to the field and after a few strong phases from the hosts, 22-year-old fly-half Piers Francis dropped a goal to trim the gap to eight.
But on 57 minutes, the visitors effectively killed the game off when replacement flanker Shane Jennings ghosted through the Edinburgh defence and offloaded to Sexton who duly crossed for the try before adding the conversion.
Edinburgh refused to buckle and concede the try bonus point however and Francis began to pull the strings, leading Leinster to take desperate measures which saw No.8 Jamie Heaslip sent to the sin bin on 65 minutes for killing the ball under the posts.
Leinster were undeterred however and Ian Madigan, on at full-back for Kearney, grabbed their fourth try of the night on 69 minutes as he finished off a fine flowing move by the visitors.
Sexton took his tally to 16 points for the night with the conversion but impressively, Edinburgh came back again and prop Willem Nel showed handling skills befitting of a dazzling back to dart over for a try.
Francis added the extras and Edinburgh went straight up to Leinster's try-line again but the visitors forced a penalty, booted clear and ran the clock down to complete an excellent win.
|Edinburgh Rugby Score Card|
|Leinster Rugby Score Card|