The province scored three tries in the first half of the derby, with a Werner Kok double and superb finish from Tom Stewart giving Ulster a 7-17 lead at the break in Dublin.
The URC Champions rallied well in the second half, with Irish international replacements coming on to make a big impact and claw back the lead.
Ireland hooker Dan Sheehan's late try was the difference in the end, with Ulster resigned to a losing bonus point for their efforts.
In a back and forth first quarter of the match, Ulster showed strong defensive resolve, ensuring Leinster couldn't capitalise on early possession.
Ulster struck first after an attack in the Leinster 22, and after a penalty advantage, fly-half Jack Murphy planted a inch perfect cross field kick over towards Werner Kok on the left wing. Kok read the bounce of the ball well and finished for the early unconverted try.
Leinster hit back soon after and took the lead, with their All-Black centre, Reiko Ioane, running in to score after a period of sustained pressure despite some superb goal line defending. Sam Prendergast's conversion gave the hosts a two point lead.
Ulster's second try was a clever piece of play involving Nathan Doak and the in-form Kok. Doak read Charlie Tector's loose pass and the scrum half hacked the ball forward into the home side's 22. Kok was chasing the ball down and was rewarded for his efforts with a try under the posts, with Doak adding the conversion.
Hooker Tom Stewart then added a third before half-time, after the ball was worked out wide to the right flank in an attack. Stewart showed great feet and strength to fend off James Lowe to finish.
At half time, Ulster took a ten point lead into the break.
Leinster soon brought on their forward replacements to bring experience and impact the game.
The away side received two early blows when both Rob Baloucoune and Charlie Irvine came off after knocks, with the returning Ethan McIlroy and Joe Hopes replacing them shortly into the second period.
It was a proud moment for McIlroy, who returned after a lengthy injury absence following an ACL injury in January.
Ulster's line speed and defensive efforts were keeping the hosts at bay in the opening exchanges, but eventually their pressure told and winger, Joshua Kenny, scored the home side's second try.
Leinster centurion, James Ryan, was given a yellow card after a dangerous clear out on replacement loosehead prop Sam Crean and Ulster were able to add three points with a well taken penalty from range from Nathan Doak.
Despite being down to fourteen, Leinster were able to show their attacking quality after gaining some territory in the Ulster 22. After some crisp passing, James Lowe was found out on the left wing for a simple finish.
Fighting to maintain the three point advantage, Ulster were then punished with a yellow card for what was deemed a deliberate knock on by David McCann, which prevented a line break.
Minutes later Leinster made their advantage count, and Ireland international hooker, Dan Sheehan, finished off a powerful lineout maul to make the match-winning difference, with Harry Byrne converting for a four point lead.
Richie Murphy's side will regroup and prepare for their second interprovincial derby of the winter period against Connacht at Dexcom Stadium in Galway next weekend.
Scorers
Leinster:
TRY: Ioane, Kenny, Lowe, Sheehan
CON: Prendergast, Byrne
Ulster:
TRY: Kok x2, Stewart
CON: Doak
PEN: Doak
Teams
Leinster:
1\. Jack Boyle, 2. Gus McCarthy 3. Rabah Slimani, 4. Brian Deeny, 5. James Ryan, 6. Alex Soroka 7. Scott Penny, 8. Jack Conan (C), 9. Luke McGrath 10. Sam Prendergast 11. James Lowe 12. Charlie Tector 13. Rieko Ioane 14. Joshua Kenny, 15. Ciarán Frawley
Replacements: 16. Dan Sheehan, 17. Paddy McCarthy, 18. Tadhg Furlong , 19. Joe McCarthy, 20. Max Deegan , 21. Fintan Gunne, 22. Harry Byrne, 23. Ruben Moloney
Ulster:
1\. Angus Bell, 2. Tom Stewart , 3. Tom O’Toole , 4. Harry Sheridan, 5. Charlie Irvine, 6. David McCann, 7. Nick Timoney (CAPT), 8. Juarno Augustus, 9. Nathan Doak, 10. Jack Murphy, 11. Werner Kok, 12. Stuart McCloskey, 13. Jude Postlethwaite, 14. Rob Baloucoune, 15. Jacob Stockdale
Replacements: 16. John Andrew, 17. Sam Crean, 18. Scott Wilson, 19. Joe Hopes, 20. Bryn Ward, 21. Conor McKee, 22. Jake Flannery, 23. Ethan McIlroy