The hosts put their Heineken Cup loss to Northampton behind them to extend their winning run in the competition to 11 successive games.
A first-half penalty try was supplemented by second-half scores from Nick Williams and Andrew Trimble in a game which Ulster had to battle hard to triumph and saw them finish with 14 men after Rory Best was yellow-carded late on.
While Ulster saw off 2012 in fitting fashion, Leinster fell to their third consecutive defeat in all competitions, which will have done Joe Schmidt's men some damage in their bid to stay pushing for the league play-offs.
Ulster really should have been out of the blocks first but Paddy Jackson's fourth-minute penalty sailed left of the posts from what was a kickable effort.
Eight minutes later, though, Ian Madigan made no mistake with his first kick after Tom Court was penalised at a scrum to get the visitors up and running.
With Leinster increasingly getting on top it came as no surprise that Madigan made it 6-0 with a second penalty after 18 minutes when Nick Williams was penalised for not rolling away.
Ulster's cause was not helped when Jackson again miscued his second effort after 23 minutes. He made no mistake three minutes later, though, to get Ulster off the mark after Court won a penalty off Michael Bent.
The scores were then levelled just before the half hour-mark when John Afoa won a scrum penalty and this time Ruan Pienaar landed the longer-range effort.
Madigan then kicked his third penalty shortly afterwards but Ulster responded with Williams leading the way and then from a five-metre scrum referee George Clancy awarded a penalty try, which Pienaar converted to put Ulster 13-9 up at half-time.
But Leinster started the second half with Jamie Heaslip making a strong burst and with their opponents off-side in their own 22, Madigan struck his fourth penalty to close Ulster's lead to a single point.
The hosts responded as a Trimble half-break led to Darren Cave, Court and Pienaar all taking it on and Ulster got over the line with the television match official awarding the score to Williams.
Pienaar converted to put Ulster 20-12 ahead after 46 minutes but the Springbok was then wide with a 63rd minute attempt as Ulster began to put real pressure on Leinster.
With 10 minutes left, Best was sin-binned for not rolling away and even though Madigan was wide with the penalty, Ulster had to close out the game with 14 men.
And this they did with Pienaar's cross-kick working a treat for Trimble, who lost Andrew Goodman to score with Pienaar slotting the conversion to make it 27-12.
Yet Leinster struck when Fergus McFadden got on the end of a Madigan pass in the 78th minute with the out half then kicking the conversion but Leinster were unable to score again and make off with a losing bonus point.
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