The Dons were held to a 1-1 draw at Pittodrie on Thursday, with the second leg in Bosnia-Herzegovina on 20 July.
Apollon hold a commanding 3-0 lead after their home first leg.
Coached by former Cyprus goalkeeper Sofronis Avgousti, Apollon finished third in their national league last season.
Their squad, which features several Cyprus internationals, includes former Sunderland centre half Valentin Roberge, while former Porto goalkeeper Bruno Vale captained the side against Zaria.
Malta striker Andre Schembri, their summer signing from Boavista, opened the scoring, with Brazilian midfielder Alex da Silva adding to that from the penalty spot before Portuguese Joao Pedro made it three before the break.
Defender Angelis Charalambous, who had a short spell with Motherwell, and 20-year-old Edinburgh-born midfielder Alastair Reynolds are also on the Apollon books but did not feature in their Europa League line-up.
Apollon went into the third qualifying round last season but lost 5-4 on aggregate after extra-time against Grasshopper Zurich.
Zaria, who finishing fourth in Divizia Nationala last season, qualified because title winners Sheriff Tiraspol completed a league and cup double.
Having themselves won the cup the previous season for the first time, Zaria were knocked out in the first qualifying round of the Europa League after also losing the first leg 3-0 to Videoton of Hungary before winning the home game 2-0.
Aberdeen were in the same section of the draw at Everton, but the English side were paired with either Slovakia's Ruzomberok or Brann of Norway.
Full Europa League third qualifying round draw

Alongside a picture of him waving goodbye, the 35-year-old Spain international wrote on Twitter: "Lived it. Loved it. Farewell beautiful game."
He won club honours with Liverpool, Real Madrid and Bayern and the World Cup and two European Championships.
Alonso told Bayern's TV channel: "It wasn't an easy decision to make, but I believe it's the right time.
He added: "I always thought it would be better to quit sooner rather than later. I still feel good, but I believe this is the right moment."
Alonso joined Liverpool from Real Sociedad in 2004 and was part of a famous Champions League victory in Istanbul in his first season as the Reds came back from 3-0 down at half-time to beat AC Milan on penalties. He also claimed an FA Cup, a Uefa Super Cup and a Community Shield during his time at Anfield.
He moved to Real Madrid in 2009 and won a second Champions League as well as the Spanish title before a switch to Germany in 2014, where he has helped Bayern win two Bundesliga titles and reach the quarter-finals of this year's Champions League - courtesy of a 10-2 aggregate win over Arsenal on Tuesday.
Alonso played 114 times for Spain and scored 16 goals as the national side won the 2008 and 2012 European Championships, either side of their maiden World Cup triumph in South Africa in 2010. His final appearance for his country came at the 2014 World Cup in Brazil.
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Apollon Limassol of Cyprus or Moldova's Zaria Balti await Aberdeen in the Europa League's third qualifying round - if they get past Siroki Brijeg.
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Bayern Munich midfielder Xabi Alonso has confirmed he will retire when his contract expires in the summer.