They led 14-6 at halftime thanks to tries from O'Brien, who dipped below his normal standards in the 2012 RBS 6 Nations, and Cian Healy with Ruan Pienaar keeping Ulster in touch.
But although they did cross in the second half Dan Tuohy, it was one-way traffic as a penalty try along with scores in the final moments from replacements Heinke van der Merwe and Sean Cronin ensured coach Joe Schmidt lifted the trophy for a second successive year.
Although Ulster made a bright start, capped by a seventh minute penalty from Pienaar, Leinster soon started to stamp their authority on proceedings and they ruthlessly demonstrated their opportunism from a turnover as O'Brien blasted over from close range.
Sexton converted but missed a straightforward penalty soon after but Leinster did get the next score when Brian O'Driscoll's offload allowed O'Brien to embark on a trademark bullocking run.
Although he was eventually halted, prop Healey wriggled his way over with Sexton converting although Pienaar responded with a long-range penalty before the break.
Ulster hopes of narrowing Leinster's lead further soon evaporated when fly-half Paddy Jackson kicked out on the full to give the champions a lineout which they fully exploited as a maul was illegally halted by Ulster - referee Nigel Owens awarding the penalty try.
Ulster did respond when centre Paddy Wallace put lock Tuohy over but the afternoon belonged to Leinster as prop Van der Merwe and Cronin ensured Schmidt's side entered the record books and gave the watching Ospreys coaches plenty of food for thought ahead of next Sunday's showdown.