In Helsinki on Thursday, the Republic of Ireland scored inside the first 15 minutes of the second half to draw level before going on to win.
This time they fell behind three minutes after the interval as Bakasetas struck.
The home side's skipper benefited as his right-footed shot spun off Scales and went past Kelleher, prompting a huge roar from the raucous crowd.
Given the emotions they have grappled with and the huge effort it took to beat England at Wembley on Thursday, it perhaps wasn't surprising that Greece's intensity waned as the second half wore on.
And their fatigue coupled with the introduction of Festy Ebosele and Jack Taylor offered the Republic of Ireland fresh impetus, with Taylor denied a debut goal when his header was flicked over by Odisseas Vlachodimos.
The Republic of Ireland's only other clear opening also fell to Taylor but the Ipswich midfielder was unable to trouble the Greek keeper after a Robbie Brady corner reached him.
Then the away side's hopes of rescuing a point late on were shattered by Kelleher's lapse in concentration, with the 25-year-old passing straight to Greece substitute Mantalos, who rounded the keeper and fired into the unguarded Irish goal.
It was another soft goal from an Irish perspective after captain Nathan Collins gifted Finland an opener on Thursday.
But unlike in Helsinki, there would be no way back for Hallgrimsson's men, who were left to reflect on a fourth defeat by Greece in the space of 16 months.
Greece, meanwhile, have boosted their bid for promotion to the top tier of the Nations League, their players holding up a shirt bearing Baldock's name at full-time on another night when they battled through emotion to deliver three points.