Pablo Daniel Osvaldo's first goal for the club put hosts Juve in front on 16 minutes before a controversial moment 20 minutes from time.
Trabzonspor substitute Henrique had a shot saved by Gianluigi Buffon and Olcan Adin scooped home Yusuf Erdogan's cut-back, but was denied as the officials decided the ball had gone out for a corner.
Paul Pogba's goal in stoppage time then added insult to injury for the Turkish side.
Dutch giants Ajax were swept aside 3-0 at home by Salzburg, who have now scored in 63 consecutive matches, a run that stretches back to December 2012. Sadio Mane and Jonathan Soriano's brace did the damage in Amsterdam.
Back in Ukraine, Yevhen Konoplyanka's late penalty gave Dnipro a 1-0 win over Tottenham, strikes from Eduardo Vargas and Antonio Barragan saw Valencia defeat Dynamo Kiev 2-0 and the game between Chornomorets and Lyon finished goalless.
Last season's runners-up Benfica have the advantage heading into their second leg with PAOK, returning from Greece with a 1-0 victory thanks to a second-half goal from Rodrigo Lima.
Bulgarian outfit Ludogorets shocked Lazio 1-0, Roman Bezjak's strike securing a famous victory in Rome before Luis Pedro Cavanda and Svetoslav Dyakov were dismissed in the second half as both sides finished with 10 men.
Sevilla drew 2-2 in Slovenia against Maribor, while Porto's match with Eintracht Frankfurt finished in the same result after the German outfit came from two goals down to give themselves a healthy chance of progressing.
Nick Viergever's strike a minute from time earned AZ a 1-0 win at Slovan Liberec, while Anzhi and Genk played out a 0-0 draw in Russia.
Elsewhere, Real Betis drew 1-1 at home with Rubin Kazan and Maccabi Tel Aviv's game with Basel ended goalless.
