Fresh from winning the European Champions Cup final last weekend, Leinster gave itself breathing space with a Joey Carbery penalty that opened up an eight-point lead at RDS Arena with four minutes to go.
Gerbrandt Grobler's converted score brought Munster back within one, and left the visitors with little more than a minute to snatch victory from the jaws of defeat.
But Munster, whose only win over Leinster at RDS Arena came 10 years ago, fell just short in its efforts, leaving the host to prepare for a final against Scarlets where it will look to complete a European and Pro14 double for the first time, a feat no team has achieved.
Leinster came flying out of the blocks and had the game's first try in just the seventh minute when James Lowe brilliantly flipped inside for Jack Conan to touch down.
A JJ Hanrahan penalty for Munster was quickly answered by Ross Byrne, and Leinster appeared destined for a certain score when Lowe broke clear down the left wing only to be denied by a brilliant covering tackle from Sam Arnold.
Munster exerted pressure in the forwards as the half wound down, but was temporarily a man down when Jean Kleyn was sent to the sin bin for a reckless wipe-out of Byrne just shy of the hosts' try line.
The visitors rode out the numerical disadvantage, and Simon Zebo showed great feet before offloading for Keith Earls to squeeze over in the left corner.
The conversion was missed and Leinster extended the lead to five points with a Carbery penalty, the same man seemingly finishing the job by splitting the posts in the closing stages.
Munster ensured a dramatic finish when Grobler stretched for the line and touched the ball off the base of the post, but, despite making its way into Leinster territory, it was unable to find another scoring opportunity.