Jose Maria Callejon opened the scoring for Jose Mourinho's men after 21 minutes, while Karim Benzema scored the second with 23 minutes of the match remaining.
The Spanish champions, fielding a full-strength team including Cristiano Ronaldo and Kaka, were rarely troubled by their Scottish opponents.
And Celtic's disheartening night soured still further by injuries to Dylan McGeouch, Daryl Murphy and Anthony Stokes.
- Karim Benzema
- Jose Mourinho
- Cristiano Ronaldo