It mattered little to the Irish side however, as they emerged 34-12 winners to help end O'Driscoll's career with silverware.
And Heaslip, who toured Australia last summer with centre O'Driscoll, admits they were desperate to beat the Warriors for their teammate.
"It was great for us to be able to send off a guy who has given so much to Leinster rugby and to Irish rugby with a trophy," Heaslip said.
"He has been unbelievable to play alongside. We knew it would not be easy and, to be fair to Glasgow, I don't think the score reflected the way the two sides played, but we are over the moon to finish like that."