The Euro 2004 champions conceded a last-minute equaliser to limp unconvincingly towards this summer's showpiece in Poland and Ukraine
Fernando Santos' men entered the encounter without a win in their last three matches and were initially under the cosh against their industrious opponents. Currently ranked 28th in the world, Slovenia started brightly early on. However, it was Greece who took the lead in clinical counterattacking fashion reminiscent of their successes at the Euro 2004 in Portugal.
They put together their first meaningful piece of football on eight minutes to free Torosidis down the right flank and the Olympiakos full-back made no mistake with a clinical low finish into the bottom corner.
The goalscorer's night ended early, however, after picking up a knock and Slovenia reasserted themselves after falling behind.
Tim Matavs was looking dangerous up top and the PSV striker dragged one wide, but Slovenia appeared to lack sufficient cutting edge to pierce Greece's stubborn rearguard.
A case in point came half an hour in when defender Miso Brecko wriggled free in the box only to pass tamely into Chalkias' grateful clutches.
A few promising moves fizzled out around striker Georgios Samaras for the Greeks, but it was Slovenia who were looking the more dangerous, with Kurtic rasping a free kick just over the bar on 40 minutes.
However, Greece rallied on the brink of half-time. Giorgios Karagounis curled a lovely effort just wide before, seconds later, Konstantinos Katsouranis went for a less subtle approach by hitting a scorching drive that flew just over.
The second-half started much the same as the first, the Slovenian's pressing without troubling Chalkias.
Karagounis was looking sprightly for the Greeks, however, and he shifted the ball beautifully onto his right-foot around the hour mark, but saw his thumping drive skim the crossbar as his team started to enjoy themselves.
However, Slovenia really should have levelled the scores on 70 minutes. Chalkias made a hash of Kurtic's free kick, but redeemed himself in splendid fashion with a point-blank save from Marko Suler's follow-up effort.
Slovenia's pressing paid off on 85 minutes when Kurtic, who looked dangerous all night from set-pieces, ripped home an effort off the post to grab a share of the spoils.
Greece's night got worse when Panagiotis Kone was sent off late on for violent conduct.
Santos will be hoping for a better performance from his side when they take on Armenia in their next friendly on Wednesday.