Replacement winger Simon Keogh popped up with a crucial try and Felipe Contepomi added a late penalty goal as defending Magners League champions Leinster overcame a 7-3 half-time deficit to take the provincial spoils.
After recent wins at home to Munster and Connacht, Ulster were hoping to complete the full set of interprovincial victories in Belfast but Matt Williams' side, despite notching a convert try through centre Darren Cave, had neither the possession or territory to force the issue.
But had they finished off a fantastic break by flanker Stephen Ferris, late in the second half, the result may well have been different.
Speaking afterwards, Williams said: "We had a magnificent try, we targeted 13, we went for him and bang.
"Next one, we got five men and Stephen (Ferris) went straight through, we should have had someone on his inside shoulder and that should have been the next try.
"And then all we had to do is patiently get one more and the game's there. Instead, kick-off after half-time, we run the ball straight in front of our sticks on three phases, turn it over, they get a scrum and score a try.
"And then we chip out of our own 22? We actually said at half-time, 'do not do a short kick-out.' It's just unacceptable from the boys.
"As I've said before, we've got five words we work on and one of them is discipline. We have to have discipline. We lost our discipline and lost our game-plan."
The Australian was quick to praise his former province for the way in which they played and eventually saw out the win.
"You've got to give Leinster credit - they did not budge off their plan. For one second of that game, they did not budge off their plan.
"They kicked magnificently and kept at it and kept their shape. They showed great patience."
Williams agreed that his players will learn from the experience of losing a tight game such as this, and that they must keep their heads the next time.
"At 18-13 we had a sniff but what did we do? We went through it last time against the Scarlets. At 16-16, in the last seconds of the game, all we had to do is get in their 22, get down their end and then we go and we've proved all along that once we get in that part of the world we've very dangerous.
"We defended with such courage and the weight of possession, I don't know the exact stats but it would have been 75% easy.
"We would have made 180-odd tackles, they would have made 40. And despite that, we were still in it and leading. 13-13 we were right there and we just had to be patient.
"There's an Australian cricket saying, 'you lose patience, you lose the battle', and that's what happened."
Despite the disheartening result - with Contepomi's final kick robbing Ulster of a losing bonus point - Williams insisted that there were some considerable positives to take forward into next weekend's game against Munster, not least the defensive display from the team.
He added: "Despite all the rubbish that's been going on at the moment about them, Leinster are a great team.
"They're the league champions, they're European contenders and when you play against great teams you only get three or four opportunities. You only get a few chinks in the armour and you've got to take them.
"Like Stephen goes through, we designed that so that there should be someone on his inside shoulder and someone on his outside - and they weren't there. There was our chance and that changes the whole game at that point.
"But the plus is we've come so far, we've come a million miles in that a real European heavyweight comes here - I know they had a couple (of players) out but so did we - and we pushed them right to the wire.
"And we walk away saying, 'well, we blew it, they didn't really win it.'
"And all that is based on our 'D'. The first three or four minutes of the game when they were hitting our line, hitting our line, hitting line and we drove them back, drove them back. It was just fantastic and we kept doing it.
"But our offence has not been smart enough."