Both sides failed to score in the first half.
Tiquinho Soares' late goal in the second half in the 89th minute gave the Greek team a narrow win at Georgios Karaiskakis Stadium.
Olympiacos increased their points to nine in Group D, reaching the UEFA Europa League Round of 16 with one match remaining.
The result means Fenerbahce will continue their European journey in the Conference League after collecting five points.
In another Group D clash, Eintracht Frankfurt drew 2-2 with Antwerp at home to stay atop the group with 11 points as they already have advanced to the last 16.
Antwerp are at the bottom of the group with two points.
Kaynak: AA_ING
