Scott McDonald scored twice, while Massimo Donati, Shaun Maloney and Chris Killen were also on the scoresheet as the Egyptian and African champions were swept aside, although Dinamo Moscow will provide a sterner test on Wednesday when it really matters.
Tony Mowbray's men have not conceded a goal in three pre-season matches and will play Tottenham on Sunday in their final Wembley Cup fixture before their European qualifier against the Russians.
Mowbray had new signing Dan Fox on the substitutes' bench after the youngster arrived from Coventry earlier in the day, while Marc-Antoine Fortune and Landry N'Guemo started in the first appearance by a Scottish club side at Wembley.
Mowbray's men should have been ahead in the early stages after McDonald fired the ball towards goal but Amir Abdel Hameed turned the effort around the post, then Glen Loovens headed over from the resulting corner with the net unguarded.
Artur Boruc was required to save when Francis Doe Forkey raced through - but Celtic still looked the more threatening and hit the woodwork twice in one move shortly after.
Fortune struck the crossbar first after muscling his way through, then Maloney hit the post when he latched onto the rebound.
The opener came in the 31st minute, with Hossan El Badry's side failing to clear the ball in defence. McDonald charged a clearance down but even then there was an opportunity to boot the ball into touch.
Instead, Donati was allowed to sneak the ball through and round Hameed before finishing.
McDonald added the second from the penalty spot six minutes later. He had earned the spot-kick himself after getting on the end of Aiden McGeady's through-ball and being brought down by Hameed.
After the break, Maloney added another, receiving the ball from McGeady before firing into the bottom corner after tricking his marker with a dummy.
McDonald curled the fourth into the top corner after cutting in from the left when Lee Naylor slid the ball to him.
Boruc was needed to prevent Mohamed Aboutraika scoring, with the Poland goalkeeper bravely spreading himself when the striker got beyond the Celtic defence.
Killen beat the offside trap to tap home with seven minutes remaining.