After three consecutive defeats in the final in the last three years, scores from back rows Shane Jennings and Heaslip sealed the win for Leinster who got their noses in front early, and stayed there.
It means that both Joe Schmidt and fly-half Jonny Sexton sign off their Leinster careers in style, completing the European and RaboDirect PRO12 double that eluded them in the previous two years.
Ulster did all they could and trailing by six points they applied the pressure for the converted try but where Shane Williams and Dan Biggar combined for the Ospreys last year to sink Leinster, this time they held firm.
Leinster flew out the blocks and scored the first try of the match after just three minutes - the newly crowned Amlin Challenge Cup champions rewarded for an early show of intent.
Sexton turned down a shot at the posts and instead kicked for the corner and Leinster produced a textbook drive after collecting the lineout, Jennings the man who dotted down.
Sexton kicked the conversion from the corner and it wasn't long before he extended his side's lead to 10-0 with Chris Henry failing to release his man, capping a chaotic early period for a stunned Ulster.
That stirred the Ulstermen into action however and some concerted pressure in the left-hand corner almost resulted in a try, only for Leinster to withstand the barrage.
On 18 minutes, Ulster missed a glorious chance to get back into the match after British & Irish Lions winger Tommy Bowe burst infield and when Darren Cave spun the ball wide to Robbie Diack, he had the simplest of finishes but Leinster got back to hold him up over the line.
On 25 minutes, Ulster finally got themselves on the scoreboard, South African scrum-half Ruan Pienaar making no mistake from the tee but Sexton responded in kind soon after to restore his side's ten point advantage.
Again Ulster came back and Pienaar made it two from two on 36 minutes but Sexton notched a crucial penalty on the stroke of half-time, ensuring Leinster earned themselves some breathing space at the interval.
Things weren't going Ulster's way and Leinster threatened to build an unassailable lead when Diack was sent to the sin bin on 44 minutes for going off his feet but then Ireland fly-half Paddy Jackson sparked the hosts for the day into life.
He scythed his way through the middle but didn't have the support required to make sure of the try, however Isa Nacewa, in his last game before retirement, was adjudged to have made a high tackle on the 21-year-old and he was shown a yellow card.
Pienaar slotted the simple penalty from in front of the posts to make the score 19-9 but with both sides down to 14.
Ulster could sense a way back into the contest and, with the wind in their sails, Pienaar trimmed the gap to seven when a superb chase from Bowe saw Leinster infringe and concede the penalty on 50 minutes.
With Diack back on the pitch but Nacewa yet to return, Pienaar brought Ulster to within four points, the closest they had been since Jennings' third-minute try, but Leinster came back, aware that they were losing momentum.
And it was Heaslip, who the help of second row Devin Tower, who burrowed his way over for another try that was borne out of forward grunt in the corner.
Sexton missed the conversion, ensuring Ulster weren't out of it, nine points down and after more good work from the impressive Rory Best, they were back to within a converted try after an enormous kick from the flawless Pienaar on 69 minutes.
With three final defeats in the last three years, Leinster were getting nervous and Ulster almost cut them open with seven minutes left on the clock, only for a knock-one at the crucial moment to cost them dearly.
Awarded a kickable penalty with four minutes left on the clock, Pienaar opted to kick for the corner and despite numerous phases in Leinster territory, Ulster conceded the penalty.
Leinster marched the play downfield and allowed the clock to tick down before Brian O'Driscoll kicked the ball out to rubber-stamp his side's victory.