Leinster ran in six tries to make it two bonus points in a row in Pool 2 and, although O'Driscoll played no part in the second half after picking up a knee injury, he is not expected to be out of action for long.
"Brian's injury does not look too serious," said Leinster coach Michael Cheika.
He just couldn't get his knee moving during the game. We made the decision to take him off even though he didn't want to go. He's taken a knock to his knee and we think it is ligament damage."
O'Driscoll gave the capacity crowd something to cheer about as early as the fifth minute when he managed to wriggle his way over to claim a try which the Television Match Official confirmed.The first of Danny Cipriani's two penalties followed, before O'Driscoll conjured up a mercurial second try.
There seemed little likelihood of him scoring when he chipped over the top of the defence on the edge of the Wasps 22 but he reached the bouncing ball, kicked it over a second defender and regathered on the line to score again. It was a phenomenal try which must have had Wasps director of rugby McGeechan purring with delight in his Lions capacity - and cursing him from a Wasps perspective.
After O'Driscoll had shown his team-mates the way, Leinster added a further four tries to leave Wasps coach Shaun Edwards with little positive to take from the game.
"It's one of our worst defeats," said Edwards.
"Normally we perform on the big stage but we're finding it quite hard to handle. The new emphasis in the game is on kicking. Their kicking game was on a different planet to ours. It's absolutely killing our game.
"We've put ourselves under huge pressure in the pool by not taking anything from this game. We have got to show our mettle and battle back from this."