Aleksandr Samedov scored for Moscow in the 45th minute. Fenerbahce's goal came from Mehmet Topal in the 83rd minute.
Fenerbahce have thus secured a spot in the Last 16.
Another Istanbul team Galatasaray bade farewell to the Europa League, losing 3-1 to Italian Lazio in an away game at the Stadio Olimpico in Rome on Thursday night.
The results of second legs are as follows:
Lokomotiv Moscow (Russia) vs Fenerbahçe (Turkey): 1-1 (first leg: 0-2)
Schalke 04 (Germany) vs Shakhtar Donetsk (Russia): 0-3 (0-0)
Athletic Bilbao (Spain) vs Olympique Marseille (France): 1-1 (1-0)
Liverpool (England) vs Augsburg (Germany): 1-0 (0-0)
Krasnodar (Russia) vs Sparta Prag (Czech Republic): 0-3 (0-1)
Lazio (Italy) vs Galatasaray (Turkey): 3-1 (1-1)
Bayer Leverkusen (Germany) vs Sporting Lisbon (Portugal): 3-1 (1-0)
Rapid Wien (Austria) vs Valencia (Spain): 0-4 (0-6)
Manchester United (England) vs Midtjylland (Denmark): 5-1 (1-2)
Basel (Switzerland) vs St-Etienne (France): 2-1 (2-3)
