The hosts were the only side to carve out any chances of note, with Alexander Ryazantsev's fierce header which goalkeeper Alexandros Tzorvas did well to turn away the closest they came to breaking the deadlock.
The Greeks barely threatened after the first minute when Tzorvas' opposite number Sergei Ryzhikov picked up a backpass, the resulting indirect free-kick coming to nothing.
The point apiece left Rubin and Pana in third and fourth place in Group D respectively, some way adrift of leading duo FC Copenhagen and Barcelona.
Rubin almost shot themselves in the foot in the opening minute when Salvatore Bocchetti's backpass sold Sergei Ryzhikov a little short and the goalkeeper had to dive on the ball with Djibril Cisse closing in.
The free-kick was teed up for the Frenchman, who drove his low shot into the wall.
At the other end Sergey Kornilenko drove in a shot to the near post from a very acute angle on the right which Tzorvas saved with his feet.
Rubin were looking the most likely to open the scoring, with the vision and quick-feet of Carlos Eduardo their best source of attacking inspiration.
And Alexander Ryazantsev brought a fine save out of Tzorvas in the 40th minute when he met a cross from the right with a powerful header on the run which the keeper got strong palms to and pushed out.
Kornilenko then made a mess of on a glorious headed chance when unmarked at the far post, not getting a good enough contact on the ball from Alan Kasaev's left-wing cross and glancing it tamely wide.
The Russians started the second half as they had finished the first and Kornilenko intelligently flicked on a low cross from the left at the near post, but no one read it and the ball flew across the face of goal.
Ryazantsev tested Tzorvas again in the 78th minute, the keeper saving his effort with his feet, and frustrated the hosts again by keeping out Cesar Navas' weak shot a minute later.
Substitute Obafemi Martins then got his leg to a Bebars Natcho free-kick but Tzorvas reacted very well to make the save from point-blank range as Rubin failed to find a way through.