Kenny Dalglish recalled Lubomir Moravcik to the side in the place of the injured Mark Viduka.
BBC: Hearts stay on Euro course
2.
Celtic made it 3-0 before half-time when Moravcik teased his way past Thomas Solberg before crashing the ball into the roof of the net with Leighton powerless.
BBC: Celtic embarrass Scottish strugglers
3.
Celtic were gifted a second goal after 34 minutes after a dreadful error from veteran keeper Leighton who misjudged a long-range effort from Moravcik and paid the price.