The defending champion defeated its Irish rival in front of a packed RDS Arena in what was for the most part an attritional semi-final.
Ireland flanker Josh van der Flier was influential on his return from groin surgery, earning the man of the match award for his brilliant work at the break down, while Ross Byrne kicked 14 points.
Sean Cronin and James Lowe tries ensured there was a comfortable-looking scoreline but Munster hung with the home side for much of the contest.
Munster was leading for much of the first half as a couple of Joey Carbery penalties cancelled out Byrne's early three-pointer and Lowe was sent to the sin bin for a deliberate knock-on.
Leinster rode out the numerical disadvantage, however, and Byrne kicked his side into a three-point half-time lead.
Niall Scannell was sin-binned early in the second half for Munster before Byrne and Carbery traded penalties once again.
The decisive moment came in the 55th minute when an overlap on the right led to Cronin touching down for Leinster.
Lowe also went over in the closing stages after the ball was worked off the back of a scrum, leaving Leinster free to prepare for next week's final at Celtic Park.