Roberto Mancini's side are now five points behind the table-toppers after they were held to a goalless draw at out-of-form Karabukspor on Friday.
Gala entered the match on the back of thrashing Akhisar Belediyespor 6-1, but their attack failed to fire on this occasion.
Despite having the second leg of a last 16 UEFA Champions League tie at Chelsea to contemplate, Mancini used star striker Didier Drogba for 89 minutes.
Wesley Sneijder and Burak Yilmaz also played full matches but they were left frustrated by a side who have not won in their last five.
That result allowed Fener to go five points clear at the top of the league thanks to a 2-1 win over Kayseri Erciyesspor on Sunday.
Former Liverpool attacker Dirk Kuyt gave Fenerbahce the lead in the 33rd minute with his ninth goal of the Super Lig season.
And although the losers responded in the 63rd minute after Edinho scored a penalty, parity did not last long.
Less than two minutes later and Fener's advantage was restored as Nigerian Emmanuel Emenike netted.
Besiktas lie third, seven points behind their table-topping Istanbul rivals, after they could only draw 2-2 at Rizespor on Saturday.
Mustafa Pektemek had given Besiktas the lead after just six minutes but first-half penalties to Leonard Kweuke and Ali Adnan saw the hosts edge in front at the break.
Pektemek's second goal – scored five minutes into the second half – saw Besiktas draw level but they could not score a winner.
Sivasspor's woes continued as they were embarrassed 4-0 at home by the fourth-placed Trabzonspor on Sunday.
Roberto Carlos' side have won just one of their last 10 matches in all competitions, suffering eight losses in that period.
Their fourth loss in a row was wrapped up by half-time as Mustafa Yumlu, Olcan Adin and Paulo Henrique all scored early goals.
Ozer Hurmaci wrapped up the win with his side's fourth goal after the break.
Elsewhere, Genclerbirligi won 2-1 at Kasimpasa and Gaziantepspor and Eskisehirspor recorded 1-0 wins over Konyaspor and Eskisehirspor respectively.
Akhisar Belediyespor and Antalayaspor played out a goalless draw and Monday's fixture saw bottom-placed Kayserispor beat 10-man Bursaspor 2-0, but they remain seven points from safety.
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