Artem Milevskiy, Dynamo's driving force throughout the match, sent Eremenko through with a diagonal cross-field pass at 20 minutes before the Fenerbahce's onrushing goalkeeper Volkan Demirel made the midfielder's finish even easier.
Fenerbahce's best chance fell to
"A coach needs a year or two to build up a good team and I have been at Fenerbahce for 5-6 months only," Fenerbahce's coach Luis Aragones told reporters.
"We didn't control the ball today and that's why we failed to create any scoring chances. Still, (we) should have moved better without the ball, especially at the back."
Claudio Maldonado of Fenerbahce was sent off for violent conduct in injury time.
Dynamo join Ukrainian rivals Shakhtar Donetsk and Metalist Kharkiv in the UEFA Cup, while group winners