They had controlled large sections of the match and at the back Henning Berg and Craig Moore were magnificent.
However, Rangers ended up cursing their luck as substitute Pantetis Konstantinidis headed home from close range.
There is no doubt Rangers would have settled for a point if was offered beforehand but having gone so far the Ibrox men will feel disappointed that they did not win the game.
One thing Alex McLeish has always displayed as Rangers manager is bravery and the alluring quality was on show again in Athens.
Some managers may have opted for caution, but McLeish played an attacking formation and got his reward.
Craig Moore came back into the skipper the side and play beside Henning Berg while Zurab Khizanishvili moved to right back at the expense of Maurice Ross.
Otherwise it was the regular line-up with Capucho and Lovenkrands in the wide areas and Arveladze and Mols up front.
It was a fearless decision and the Rangers players displayed the same qualities as they roared to a half-time lead.
Sure, there were some hairy moments, most notably when Raimondas Zutautas beat Stefan Klos with a right foot shot but Mikel Arteta was perfectly positioned just in front of the line to head clear.
But Rangers had looked in the mood from the opening moments. Indeed they might have scored after just three minutes.
Arveladze and Mols combined magnificently with the excellent Mols laying the ball off to his strike partner who had burst into the box but Arveladze shot wide of the left hand post.
Rangers came desperately close to scoring in seven minutes when Capucho won a free kick on the right side of the box.
Arteta produced a terrific delivery, driving the ball across the face of the six yard box. It only needed a touch and the net would have been bulging but if flew agonisingly past every Rangers player.
The Greeks were rattled and that was evident in 15 minutes when Silvio Maric was booked for a tackle from behind on Emerson. The Brazilian was to exact considerable revenge.
With nearly 35 minutes on the clock, Mols slid the ball down the right flank for Capucho, who was played onside by Giorgios Seitaridis on the other side and Panathinaikos were in real trouble.
Capucho burst forward, delivered a low cross into the box and Emerson bundled the ball into the net from close range to send the band of Rangers fans into raptures.
It was Rangers’ first goal on Greek soil and it was so vital.
Two minutes later and Rangers might have gone two up. Peter Lovenkrands cut in from the left and tried to thread a pass through to Arveladze who would surely have scored but Nasief Morris stretched out his right boot and just managed to clear for a corner.
The Greeks were forced into a change at half-time when Sotirios Kyrgiakos had to go off and he was replaced by Ioannis Goumas but the substitute was not long for the game.
He was booked for a wild challenged on Lovenkrands in 47 minutes and then he was sent off for a second yellow just nine minutes later for tugging the shirt of Arveladze.
It seemed like a harsh decision and the Greeks responded through a sense of injustic to put Rangers under pressure.
Giant Cypriot striker Michael Konstantinou tested Klos with a fierce drive in 64 minutes which the Rangers keeper could only push away.
Then in 71 minutes Henning Berg, who was immense all night, had to make a brilliant block to deny substitute Dimitris Papadopoulos a real scoring opportunity.
There was another scary moment when Klos kicked the ball staight at Papadopoulos but fortunately the Greek striker slipped and Klos was able to recover.
However, with just two minutes remaining Rangers were cursing their luck when Panathinaikos managed to find an equaliser.
Konstantinou touched the ball to the side for Papadopoulos who tried to shoot but fired the ball into the ground and it bounced up perfectly for fellow sub Pantetis Konstantinidis who headed into the net from close range.
It was a bitter blow to the Scottish champions because they had deserved to win it, but the now top Group E going into the double header with Manchester United.
PANATHINAIKOS: 12-Chalkias; 5-Seitardis, 3-Morris, 16-Kirgiakos (8-Goumas 45), 30-Fissas; 35-Michaelsen, 10-Epalle (27-Konstantinidis.
79), 14-Zutautas, 4-Maric; 19-Konstantinou, 7-Vlaovic (11- Papadopoulos 63)
Subs not used: 1-Nikopolidis, 6-Munch, 18-Sanmaerten, 20-Basinas.
Sent off: Goumas (56)
Bookings: Maric (15), Vlaovic (42), Epalle (60)
RANGERS: 1-Klos; Khizanishvili, 3-Moore, 25-Berg, 18-Ball; 20-Capucho, 4-Emerson, 23-Arteta, 26-Lovenkrands (16-Vanoli 76); 7-Arveladze, 10-Mols (8-Nerlinger 84).
Subs not used: 22-McGregor, 9-Ostenstad, 12-Malcolm, 21-Ross, 27-Hughes.
Bookings:
Ref: Arturo Dauden Ibanez
Att: 13,718