But O'Driscoll ensured the home side had the last laugh, grabbing the decisive score in the 70th minute.
Isa Nacewa converted O'Driscoll's effort to add to his two earlier penalties as second-bottom Leinster successfully turned the Magners League table on its head by beating title-challenging Munster.
The Ospreys narrowly overcame Scarlets 21-18 in an error-filled affair at Llanelli's Parc y Scarlets to win their fifth straight game against their Welsh rivals.
Richard Fussell and Alun Wyn Jones grabbed the tries for the visitors and Dan Biggar kicked the winning drop goal while Stephen Jones kicked six penalties for all of the home side's points.
Elsewhere Allan Jacobsen's converted try lifted Edinburgh to a 10-9 win on Italian soil against Aironi.
The Scots trailed 6-3 at the interval with just a David Blair penalty to cheer about but prop Jacobsen touched down with just four minutes left and Blair added the extras for the narrow win.