O'Driscoll showed his trademark poacher's instinct from a close-in ruck in the 71st minute, nipping in by the posts after a mammoth 27 phases of patient carrying and ruck control from the visitors.
Ian Madigan kicked five penalties and a conversion for Leinster, while Ian Keatley and Felix Jones went over for Munster. Keatley added two penalties.
Fly-half Dan Biggar scored 18 points as the Ospreys climbed back into the RaboDirect PRO12 play-off places with a 28-3 victory over Treviso at the Liberty Stadium.
The Ospreys, who had tries through wing Ben John, Biggar and scrum-half Rhys Webb, failed to get the bonus point but knocked rivals Scarlets back down to fifth place.
Treviso scrum-half Tobias Botes opened the scoring on seven minutes with a penalty after Joe Bearman was caught offside in front of his posts.