Ulster’s setbacks started even before a ball had been kicked at the Aviva Stadium as Ireland centre Stuart McCloskey was forced to withdraw.
Stewart Moore was promoted to the starting line up, with Wilhelm De Klerk coming onto the bench.
Moore only lasted 15 minutes before going off injured and matters were made worse when Mike Lowry had to leave the field five minutes later after a heavy collision.
With only two backs on the bench Murphy had to reshuffle his deck with Nathan Doak moving to full back.
Ulster started brightly dominating the early exchanges in terms of territory and possession and were rewarded with the opening score when they forced a penalty in front of the Leinster posts that Jack Murphy slotted over with the simple kick.
Leinster struck on 19 minutes, centres Robbie Henshaw and Garry Ringrose combining to put Tommy O’Brien into space. The winger advanced before chipping over Doak and had enough pace to win the race, gather the ball and touch down for an unconverted try.
The home side’s second try arrived in the 27th minute, after a lineout, number eight James Culhane drove from the line but was stopped short. The forwards patiently worked the ball through five phases before prop, Tom Clarkson, squeezed over from close range, with Ciaran Frawley adding the conversion.
Ulster unlocked the Leinster defence on 36 minutes with a cleverly worked try for Cormac Izuchukwu.
Doak soared high in the air to take a John Cooney box kick and presented the ball quickly for the replacement scrum-half, who put Izuchukwu through a gap and the Irish international playing his first game in two months after returning from injury, galloped with pace to go under the posts. Murphy landed the conversion.
Leinster went into the interval with a 19-10 lead after they were awarded a penalty try in the last minute of the first half.
The hosts kicked a penalty to touch, the forwards set up a driving maul that was surging towards the line when the referee adjudged Dave McCann pulled it down illegally, which earned the Ulster number eight a yellow card and the referee awarded Leinster the seven points.
HT: Leinster 19-10 Ulster
Leinster wrapped their try bonus point up two minutes after the restart, the backs moved the ball quickly to expose Ulster’s numerical disadvantage and Jamie Osborne put Garry Ringrose over in the corner for an unconverted score.
Leinster lock Diarmuid Mangan was sin binned on 51 minutes for lifting a player above the horizonal at the ruck.
Tommy O’Brien created Leinster's fifth try on 58 minutes, the winger collecting the ball in the Ulster 22 and kicking to the wing, where replacement hooker Dan Sheehan was unmarked and went over for an unconverted try.
Sheehan scored his second try on 68 minutes, Liam Turner made a break and was hauled down close to the line, the forwards worked the ball through a couple of phases before the Ireland international hooker powered over with Sam Pendergast converting.
Replacement lock, Matty Dalton, grabbed a late consolation try for Ulster from close range with Murphy converting.
Leinster finished with a flourish as Sheehan collected his hat trick try with two minutes remaining for bring the contest to an end.
Scorers
Leinster
Tries: Tommy O’Brien, Tom Clarkson, Penalty Try, Garry Ringrose, Dan Sheehan x 3
Cons: Ciaran Frawley, Sam Pendergast
Pens
Ulster
Tries: Cormac Izuchukwu, Matty Dalton
Cons: Jack Murphy x 2
Pens: Jack Murphy
Teams
Leinster:
15\. J Osborne; 14. T O'Brien, 13. G Ringrose, 12. R Henshaw, 11. J O'Brien; 10. C Frawley, 9. L McGrath; 8. J Culhane, 7. S Penny, 6. A Soroka, 5. D Mangan, 4. J McCarthy, 3. T Clarkson, 2. G McCarthy, 1. J Boyle
Replacements:
16\. D Sheehan for G McCarthy 46 mins, 17. A Porter for Boyle 46 mins, 18. T Furlong for Clarkson 46 mins, 19. R Snyman for J McCarthy 52 mins, 20. M Deegan for Snyman 70 mins, 21. F Gunne for McGrath 60 mins, 22. S Prendergast for Henshaw 61 mins, 23. L Turner for T O’Brien 61 mins
Ulster:
15\. M Lowry 14. Z Ward, 13. J Postlethwaite, 12. S Moore, 11. J Stockdale; 10. J Murphy, 9. N Doak, 8. D McCann, 7. N Timoney, 6. J McNabney, 5. C Izuchukwu, 4. A O'Connor, 3. T O'Toole, 2. R Herring, 1. A Warwick
Replacements:
16\. T Stewart for Herring 41 mins, 17. C Reid for Warwick 38 mins, 18. S Wilson for O’Toole 56 mins, 19. M Dalton for Izuchukwu 47 mins, 20. K Treadwell for O’Connor 47 mins, 21. Cooney for Lowry 20 mins, 22. W De Klerk for Moore 15 mins, 23. M Rea for McNabney 60 mins, O’Toole for Reid 61 mins
Ref: G Gnecchi (FIR)