Ricardo Quaresma scored the only goal for the Black Eagles on a spectacular free kick in the 29th minute at the Vodafone Arena in Istanbul.
Dynamo Kyiv’s goal came in the 64th minute from Viktor Tsygankov who entered the match in the 61st minute, replacing Derlis Gonzalez.
In the other Group B match, Napoli beat Benfica 4-2 at the San Paolo Stadium.
Besiktas is in second place in the group with 2 points and will play Napoli on Sept. 19 in Italy. Dinamo Kyiv will take on Benfica in Ukraine.