Egeman Korkmaz scored the only goal of the clash at Sukru Saracoglu Stadium in Istanbul as Aykut Kocaman's side got the job done in front of their home fans.
The goal came in the 72nd minute, in controversial circumstances, as Fener were awarded a corner which potentially should not have been given.
However, the ensuing ball was played into the area for Korkmaz to rise above his marker and head home off the bar to give the Turkish side the edge.
Fenerbahce were unlucky throughout, striking the woodwork on three occasions, including Cristian's first-half penalty not beating the post but they had to wait until there was 18 minutes remaining to get their noses in front.
2012/13 UEFA Europa League semi-final - first leg
Sukru Saracoglu Stadium, Istanbul