Pana began the campaign with a 5-1 drubbing at the hands of Barcelona and remain winless in Group D after goals from Dame N'Doye and Martin Vingaard sealed a deserved victory for the Danish champions.
- Panathinaikos 0-2 FC Copenhagen: As it happened
Nikos Nioplias' hosts played much of the second period with 10 men after Brazilian veteran Gilberto Silva picked up a red card on 52 minutes for a second bookable offence.
The win maintains Copenhagen's bright start to the group phase, and they sit top of their section with a 100% record following their 1-0 win over Rubin Kazan two weeks ago.
The hosts wasted no time getting in the first shot of the night, less than 30 seconds on the clock when Djibril Cisse unleashed a long-range effort which required Johan Wiland to tip over.
With nine minutes gone the Greek side went close again, this time Sotiris Ninis seeing his well-struck free-kick saved by the alert Wiland.
It was all one-way traffic in the early exchanges as Pana looked hungry to recover from the hammering at the hands of Barcelona on matchday one, and with 17 minutes on the clock Wiland was again called into action as Ninis let fly from distance.
And the Copenhagen goalkeeper produced his best moment of the half four minutes later, making a diving save to divert Loukas Vyntra's goalbound effort out for a corner.
Wiland's exploits were rewarded on 38 minutes when the visitors went into the lead through Pana old boy N'Doye, who picked up Vingaard's pass and unleashed a fine shot beyond Alexandros Tzorvas.
Copenhagen doubled their lead after 36 minutes from a free-kick awarded after Gilberto Silva had upended N'Doye, resulting in the midfielder's first booking of the night.
Vingaard stepped up to take the resulting set-piece, and left Tzorvas grasping at thin air as he dispatched a delightful effort into the bottom-left corner.
Panathinaikos threw on Kostas Katsouranis for Giorgos Karagounis at the break in a bid to turn the tide, but within minutes of the restart the home side's hopes faded still further with the dismissal of Gilberto Silva, who picked up a second booking for handball.
Pana's forays forward became increasingly fraught as they battled against their numerical disadvantage, and Cisse's hopeful shot from distance, which was charged down by Mikael Antonsson, underlined the desperation in the home side's ranks.
The visitors were by now dictating the play and might have gone further ahead on 62 minutes when N'Doye fired wide of the upright from inside the area.
Hjalte Bo Norregaard went closer to adding a third eight minutes later when his effort from close range smacked against the crossbar, while Pana's swift counter-attack following that scare ended with Cisse firing just wide of the right-hand post.
There was still time for Cisse to fire in another effort for the hosts inside the final 15 minutes, but again the French striker was wayward as Panathinaikos' night ended in frustration.