Scholes and Smith were keen to shoot on sight, and Gabriel Heinze went close with a free-kick as Sir Alex Ferguson's men attempted to improve their advantage.
The Greeks continued their shoot-on-sight policy as the second-half unfolded and Karagounis brought out the best in McGregor again with a powerful drive.
Rangers were seldom seen as an attacking threat and their only sight of goal in the first half came when Sebo turned nicely on a Brahim Hemdani pass only to shoot tamely at Artur Boruc.