Trabzonspor beat AEK Athens 3-1 at the OAKA Spyros Louis Stadium in the Europa League first-leg clash in Greece on Thursday.
AEK took on early lead when Livaja found the back of the net on four minutes.
Caleb Ekuban equalised for Trabzonspor on 29 minutes and bagged a brace just before half-time to give his side the lead heading into half-time.
The Ghana international scored his hat-trick on 70 minutes with 20-year-old wonderkid Abdulkadir Omur providing an assist to give Trabzonspor a major advantage heading into the second leg next Thursday in Turkey.
The 25-year-old who joined Trabzonspor on a permanent move from Leeds United over the summer – after spending last season on loan.
Ekuban now has four goals in four games for the Black Sea based outfit.
Omur meanwhile has two assists in his first four games of the season for Trabzonspor.
The Claret-Blues take on Malatyaspor at home next in the league before the second-leg of the Europa League against AEK next Thursday again at home.
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AEK 1-3 Trabzonspor
Stadium: OAKA Spyros Louis
Referee: Daniel Siebert, Rafael Foltyn, Jan Seidel (Germany)
AEK: Barkas, Paulinho, Vranjes, Svarnas, Lopes, Simao (min. 63 Krsticic), Simoes, Verde (min. 65 Geraldes), Livaja, Mantalos, Oliveira (min. 84 Giakoumakis)
Trabzonspor: Uğurcan Çakır, Pereira, Hüseyin Türkmen, Hosseini, Novak, Abdulkadir Parmak, Sosa, Abdülkadir Ömür, Nwakaeme (min. 72 Avdijaj), Ekuban (min. 90+2 Yusuf Sarı), Sörloth (min. 77 Doğan Erdoğan)
Goals: min. 4 Livaja (AEK), min. 29, 44 & 70 Ekuban (Trabzonspor)