Midfielder Beram Kayal scored a second in the 54th minute with a deflected shot to give the home side a cushion.
In the 88th minute Hoops substitute Nir Biton, who replaced Mikael Lustig, was shown a straight red card by referee Ivan Bebek for his challenge on Thulani Serero before Ajax substitute Lasse Schone grabbed an injury-time consolation.
The Scottish champions have three valuable points from three fixtures ahead of their trip to Amsterdam in a fortnight's time.
The Hoops went into the game without suspended skipper Scott Brown and injured duo, Kris Commons and Adam Matthews, but they showed they had more than enough quality left for the Dutch side.
Ajax defender Christian Poulsen hit the post in 29 minutes but that aside, there was no real pressure on the Hoops goal in the opening period.
Fraser Forster made a crucial save from Serero just before Celtic got the second but the home side were well worth their win and can travel to Holland with confidence.
- Sports & Recreation
- Anthony Stokes
- Thulani Serero
- James Forrest