Gerbrandt Grobler’s late try set up a nerve-jangling final minute, but the European Champions Cup winners prevailed.
A seventh-minute try from Jack Conan was the difference between the sides at half-time, Leinster establishing a 10-3 lead with JJ Hanrahan and Ross Byrne exchanging penalties.
A momentum-shifting try from Keith Earls, two minutes into the second half, took the heat out of Jean Kleyn’s sin-binning, only for Byrne’s second penalty and a 76th-minute penalty from Joey Carbery to prove just enough for the hosts.
James Lowe quickly made his mark, with his slick offload sending Conan over to the left of the posts. Carbery converted and the omens were not good for Munster, a knee injury forcing Jack O’Donoghue off.
Hanrahan and Byrne swapped penalties before the abrasive visitors saw lock Kleyn’s reckless clear-out on Byrne result in a yellow card. Munster roared back after the restart, Earls touching down near the left corner. Replacement Ian Keatley’s missed conversion was followed by a Byrne three-pointer at 13-8.
Leinster’s reserve front row were hugely influential, with Andrew Porter delivering a crucial scrum penalty which Carbery landed for 16-8.
Munster stormed back and TMO Neil Paterson confirmed Grobler’s try. Keatley’s conversion had the margin down to a single point, but Leinster replacement Max Deegan latched on to a ruck ball to force a final penalty and end Munster’s comeback bid.