The Italians scored either side of half-time allowing them to look ahead to the return leg in Trabzon with confidence knowing they have a two-goal lead.
Dani Osvaldo, who joined the Bianconeri on loan from Southampton on deadline day, netted his first goal in his new colours when he slotted home in the 15th minute after Carlos Tevez's pass had deflected into his path.
Antonio Conte's Old Lady were searching for a second but almost conceded with 20 minutes remaining when Olcan Adin finished from close range only for the goal to be disallowed as the linesman judged the ball to be out when Yusuf Erdogan played the pass.
That decision proved costly for the Turkish side as Paul Pogba curled home a lovely effort from Tevez's cut-back in injury-time to give Juve a nice boost ahead of the trip to the Huseyin Avni Aker next week.
2013/14 UEFA Europa League - Round of 32 first leg
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