With the game knotted at 6-6, Athinaikos went on a 15-2 run spanning 3:40 for a 21-8 lead.
At half-time, Sony Athinaikos led 41-29. An 11-0 spurt at the start of the third quarter put the Greeks into a 52-29 advantage and they pulled away for a decisive triumph.
Greece national team point guard Dimitra Kalentzou excelled with 13 points and seven assists for Athinaikos, who host the second leg next week.
Seat Györ turned on the style in the second half of their opening encounter with Lemminkainen.
Trailing 36-29, Seat outscored their Lithuanian hosts 20-10 in the third quarter and pulled away for a 74-60 victory.
Hajdana Radunovic had 25 points and 11 rebounds in defeat.
Patrycja Gulak helped Energa Torun with nine points and nine rebounds in a 64-61 triumph over Dynamo Kyiv.
Poland international Agata Gajda, who put Torun in front to stay with a lay-up 7:10 from the end, scored 15 points in the victory.
Her teammate, Monika Krawiec, contributed 14.
Oxana Zakalyuzhnaya and Nadezhda were too much for Hatis Yerevan in their opening Sixteenth-Finals game.
Zakalyuzhnaya dominated with 25 points and 16 rebounds in an 80-69 victory for the Russian club.
Istanbul was a happy hunting ground for Dynamo Kursk, who won 95-69 over Besiktas.
Jillian Robbins scored 20 points and hauled in 12 boards for Dynamo.
K.V. Imperial AEL had no trouble at home with Dunav Econt Ruse, routing the visitors 93-65.
Daliborka Vilipic finished with 25 points for the winners.
Romy Bär, Petra Manakova and Tyresa Smith were unstoppable for Saarlouis Royals in their 95-71 hammering of hosts Dexia W Namur.
Germany's Bär had a team-high 25 points, Czech Republic international Manakova 21 and American forward Smith contributed 14 points and 13 rebounds.
Natalia Vodopiyanova hit a jump shot with 27 seconds remaining to lift Dynamo Moscow to a 62-61 win at Sdent Sierre Basket in Switzerland.
Evgeniya Teplyashina tried to give the hosts a first-leg lead but missed a three-pointer at the buzzer.
Vodopiyanova hit a team-high 16 points and pulled down nine rebounds.
Also for the winners, Marina Kuzina scored 14 points and grabbed 10 rebounds and Ekaterina Sytnyak finished with 10 points and nine rebounds.