Madrid came close after 15 minutes when Cristiano Ronaldo fired his shot into the side netting. Los Blancos were ahead soon after, however, as Callejon slid the ball past Zaluska.
Zaluska denied Ronaldo towards the end of the first half before Joe Ledley almost levlled the sides on the stroke of half time.
Ronaldo was once again denied by the Celtic defence towards the start of the second half, but Karim Benzema soon doubled Madrid's lead by putting the ball past Zaluska's outstretched foot.
Di Maria came close to extending Madrid's lead even further at the end of the half, but his shot went just wide as the Spanish giants ran out 2-0 winners.