The European champions had a penalty try as well as touchdowns from Gordon D'Arcy, Jonny Sexton and Ian Madigan, plus 11 points from Sexton's reliable boot.
The hosts, for whom this was a fourth successive defeat in all competitions, had two penalties by Greig Laidlaw and a drop goal from Piers Francis, who added the conversion of a late try for prop Willem Nel.
The visitors had the better of the opening 10 minutes but failed to make their territorial superiority show on the scoreboard - the closest they came being a thwarted effort by D'Arcy after the centre was set free by Sexton.
Edinburgh's first visit to the opposition half came when they earned a penalty after 16 minutes, with Laidlaw steering his kick between the sticks.
Leinster squared matters two minutes later when Sexton booted a penalty awarded for a high tackle on Brian O'Driscoll by home prop Allan Jacobsen.
Although Sexton was wide with his next effort from long range, the Irish outfit continued to enjoy the bulk of the possession and the home defence - which had been cruelly exposed in the festive derbies with Glasgow - held firm.
A score appeared inevitable, however, and it came after 34 minutes. Luke Fitzgerald broke from deep and carried play into the Edinburgh half where Leinster earned a penalty.
That was despatched into touch and when Dave Denton pulled down the ensuing maul, he was sent to the sin bin and Leinster were awarded a penalty try which Sexton converted.
Things got even better for the visitors two minutes before the break when the home defence was stretched to breaking point and Sexton fired out a long pass to D'Arcy who strolled over.
Sexton's conversion extended the lead to 14 points although Laidlaw landed a second penalty for the hosts with the final play of the first half for a 17-6 interval scoreline.
The Irishmen resumed in the same vein and appeared to have bagged a third try when Cian Healy darted over. However, his touchdown was chalked off for blocking.
Edinburgh lost Stuart McInally and Tim Visser through injury but they clawed their way back into the game when Francis landed a drop goal.
But Leinster struck back with a simple move that carved open the home defence, Sexton exchanging passes with Shane Jennings before galloping in at the corner and slotting the conversion to extinguish any hopes of an Edinburgh fight back.
Nevertheless, the hosts rang the changes and appeared set to score when Jamie Heaslip played in the ball in a ruck a couple of metres shy of the Leinster line, earning a yellow card for his trouble.
Yet, even while operating a man short, the visitors secured the bonus point try with a multi-phase move that ended with Madigan slicing through to touch down beside the posts and leave Sexton a simple conversion.
Edinburgh had the final word and rounded off a disappointing evening with a flourish.
Nel earned plaudits when he thundered over from 40 metres five minutes from the end and Francis booted the extra two points, although even that effort failed to tarnish the gloss on Leinster's four try show.
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