Despite an early effort from Tim Sparv drifting wide for the Finns, Greece looked more threatening in attack as first Panagiotis Tachtsidis blazed over from a corner before Stefanos Athanasiadis missed the target from a tight angle.
The hosts continued to press for a goal before the break and nearly got it when Kari Arkivuo fired his effort wide.
Within moments of the restart, Alexander Ring was against testing Karnezis as the Panathinaikos stopper produced a save to keep out the midfielder.
However, the home side's determination was rewarded soon after when Kasper Hamalainen played in Hurme and the forward coolly slotted into the net.
Joel Pohjanpalo also came close to a late winner for the hosts, but both sides were forced to settle for a point that leaves Greece still looking a first victory of this campaign.