Vukovic delivered a solid performance for Genk as they cruised to victory against their Turkish opponent to take a two point lead at the top of Group I.
The former Sydney FC goalkeeper made a number of good saves for Genk in the match but it was his distribution which really stood out in the win.
Genk took the lead after 23 minutes when Mbwanna Samatta slammed the ball into the back of the net with a well timed side foot volley to finish a looping cross from Joakim Maehke on the wing.
Samatta and Maehle were at it again in the second half as the pair combined onece again to double Genk's lead.
The Tanzanian international was in the right place at the right time to fire home after Maehle won the ball deep in his own half before charging up the wing and delivering another perfect cross.
It was proving to be a tough night at the office for Besiktas keeper Lloris Karius who had few answers for what Genk was throwing at him.
Former Brazil international Vagner Love gave Besiktas hope when he scored in the 74th minute, but Genk fired back almost straight away with Samatta adding an assist to his name as he set up Dieumerci N'Dongala to make it 3-1.
Vukovic helped Genk wrap up the win when he started a brilliant length of the field move which was finished off by Jakub Piotrowski to make it 4-1.
Love claimed a late consolation goal but it was too little too late for Besiktas as Genk secured their second win from three Europa League matches.
It was a less enjoyable result for fringe Socceroos defender Alex Gersbach who played 90 minutes for Norwegian club side Rosenborg as they went down 3-0 to Salzburg.
It was a rare start for the 21-year-old Sydney product who has failed to feature much this season for his club side.
Rosenborg held out a determined Salzburg attack early but their resolve was finally broken in the 34th minute when Moanes Dabour gave the home side a 1-0 lead.
Hannes Wolf gave Salzburg a 2-0 lead just after the restart before Dabour claimed his second from the spot to wrap up the 3-0 victory.
Rosenborg remain at the bottom of Group B with zero points after three games.
Finally Socceroos striker Apostolos Giannou started and played 63 minutes in AEK Larnaca's 1-1 draw with Europa League rivals Ludogrets.
