The 22-16 away win means Leinster jump above Glasgow into second place in the RaboDirect Pro12 with two rounds of fixtures left in the regular league season.
Glasgow are now third, one point behind the Irish side. The top four qualify for the play-offs with the top two enjoying home advantage in the semi-finals.
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.
Munster, six days after their Heineken Cup heroics against Harlequins, tired in the closing stages at Thomond Park and Leinster, driven on by man-of-the-match Isaac Boss, got the decisive score to keep on track for a home semi-final.
Ian Madigan kicked Leinster’s other points via five penalties and a conversion in front of watching Lions coaches Warren Gatland and Rob Howley.
In Swansea, stand-off Dan Biggar scored 18 points as the Ospreys climbed back into the play-off places with a 28-3 victory over Treviso at the Liberty Stadium.
The Ospreys, who scored 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.
Cardiff Blues regained eighth place in the table following a 28-13 victory over Zebre in a mud-fest at the Arms Park.