Alvaro Morata's spectacular goal in the first half was cancelled out by Anastasios Bakasetas from the penalty spot as the 2004 Euro champions eked out an unexpected point.
La Roja were in complete control in the opening stanza. Despite not creating too many gilt-edged attacking opportunities, Spain went ahead after Morata coolly finished from close range.
Substitute Inigo Martinez then conceded a penalty for a rash challenge on Carlos Zeca, which Bakasetas converted, to equalise for the Galanolefki.
The goal seemed to knock the winds out of Spain's sails, as the home side looked insipid thereafter and struggled to break down their visitors.
A draw means Spain now trail Sweden, who beat Georgia, after the opening matchday of qualifiers. They will look to get their campaign off and running in Tbilisi on Sunday.
On that note, let's have a look at the player ratings for Spain:
Unai Simon - 6/10
It was turning out to be a comfortable night for the Athletic Bilbao custodian till Bakasetas netted the penalty. Unsi Simon couldn't keep that out but was never really tested from open play.
Marcos Llorente - 6/10
Operating from a more withdrawn role on the night, the Atletico Madrid star showed his creative side. Marcos Llorente made some fine overlapping runs and linked up with Koke and Ferran Torres down the right side for Spain.
Eric Garcia - 7/10
What a statement performance from the soon-to-be-Barcelona player! Eric Garcia was rock solid in defence and showed his leadership skills by being a more vocal figure on the field. The Spain international completed a staggering 98% of his passes too.
Sergio Ramos - 7/10
The veteran Spain player displayed his usual nonchalance and tried pushing upfield. That gave the likes of Koke a license to roam and switch play with Ferran Torres. However, Sergio Ramos was taken off at half-time.
Jose Gaya - 7/10
After a quiet first half, Jose Gaya burst to life in the second. He became a wellspring of excellent crosses, which created a few good chances for Spain.
Rodrigo Hernandez - 7/10
Rodrigo Hernandez saw more of the ball than any other Spain player on the night. He used that efficiently while also acting as a protective cover for the back four. Rodri won four aerial duels and completed 91% of his passes.
Ferran Torres - 6/10
It was a disappointing game for the budding Spanish star, as he failed to get a shot away. Ferran Torres looked like a pale shadow of his illustrious self which ripped through Germany a few months ago.
Koke - 7/10
Koke looked to make something happen by dropping into pockets of space and laying accurate passes. He also assisted Morata with a perfectly-weighted pass over the Greek defence, which helped Spain open the scoring on the night.
Sergio Canales - 6/10
Sergio Canales' passes were accurate but not incisive. The Real Betis man completed a few tackles, though.
Dani Olmo - 6/10
Dani Olmo smashed an effort against the crossbar just before Spain's goal. But there was nothing special about his performance otherwise.
Alvaro Morata - 7/10
The Juventus target man continued his fine season with a goal on the international stage too. Alvaro Morata showed brilliant control and measured finish in the first half to score Spain's opener.
Ratings of Spain Substitutes:
Inigo Martinez - 4/10
Inigo Martinez replaced Ramos at the break and conceded the penalty with a careless foul on Giorgos Masouras, which allowed Greece to get back in the game.
Bryan Gil - 6/10
Bryan Gil played some neat passes and made a few tidy dribbles in a promising debut.
Thiago Alcantara - 6/10
It was not the most inspiring of performances from the Liverpool talisman, as Thiago Alcantara's passing was underwhelming on the night.
Pedri - 6/10
Another Spain debutant, Pedi, couldn't make much of an impression, though.
Mikel Oyazabal - 5/10
Mikel Oyazabal got the chance to score just moments after coming on but was denied by a fine last-ditch challenge by Tsimikas as Spain failed to find a winner.