The Senegalese, who spent the 2007/08 season with Pananthinaikos, put Copenhagen ahead in the 28th minute with Martin Vingaard adding a second eight minutes before half-time.
A miserable night for Panathinaikos was completed when former Arsenal midfielder Gilberto Silva was sent off after receiving a second yellow card for a handball.
The result, coupled with Barcelona's 1-1 draw at Rubin Kazan, pushed Copenhagen to the top of the group with six points.
Nikos Nioplias' Greek champions took the initiative at the Olympic Stadium with Djibril Cisse forcing a spectacular flying save from Johan Wiland after just 30 seconds with a fierce long range volley.
Despite that early promise, it was the visitors who settled quicker while Panathinaikos, with Silva operating in central defence in the absence of the injured Cedric Kante, looked vulnerable.
Copenhagen grew in confidence and went in front through their first meaningful attack in the 28th minute.
Former Chelsea winger Jesper Grønkjær was the architect, supplying a superb through ball for N'Doye, whose clever run exposed the hosts' rearguard.
Panathinaikos goalkeeper Alexandros Tzorvas made the mistake of rushing out too far and N'Doye clipped the ball past him with ease.
The Danes continued to control proceedings and went two goals up in the 37th minute when Silva fouled N'Doye 20 metres from goal. Vingaar stepped up and fired a low shot into Tzorvas' bottom right corner.
Claudemir then passed up a great chance to make it 3-0 when he fired over following a neat passing move.
Panathinaikos coach Nikos Nioplias brought on Giorgos Karagounis and Nikos Spyropoulos at half-time but frustration was getting the better of the hosts.
Silva was sent off in the 49th minute when he stuck out an arm to block a through ball. From then on it was always going to be a difficult task to haul themselves back into the match and Copenhagen comfortably held on.
