TTT Riga led by as many as 10 points in the fourth quarter but weren't able to deliver the knockout punch as Fenerbahce claimed a valuable win on the road.
Cappie Pondexter had 23 points and Turkey national team center Nevriye Yilmaz scored 11 while also pulling down nine rebounds as the Turkish giants won 59-55.
Fenerbahce had plenty of chances to surrender in this one but they battled hard in the fourth quarter to earn their sixth win in eight Group A games.
TTT Riga will be wondering just how this victory escaped them.
Latvian national team playmaker Zane Eglite nailed a three-pointer with 6:05 remaining for a 51-41 lead, but Riga were outscored 18-4 the rest of the way.
And it was Pondexter who did most of the damage in the comeback for Fener.
Her three-ball cut the deficit to 51-47, and after a made jump shot by new signing Sviatlana Volnaya from Dynamo Moscow again reduced the arrears to four at 53-49, Pondexter struck again to make it 53-51.
Riga's new signing, Portuguese international and former Spartak Moscow Region playmaker Ticha Penicheiro, sank a jumper for a 55-51 lead with 1:51 remaining.
But a Pondexter three-ball pulled the Turkish team to within one and then her jump shot with 35 seconds to go gave Fener a 56-55 advantage.
Volnaya then paid dividends with her defense, stealing the ball from Tare which led Riga's Brazilian forward Micaela Martins Jacintho fouling Pondexter.
The former star at the Rutgers University made two free throws for a three-point lead just 15 seconds from the end.
Riga still had a chance to tie with a three-ball, but Jacintho missed from long range.
Penicheiro fouled Volnaya with two seconds remaining, and the Belarus star split two at the line as Fener won by four points.
Iciss Tillis finished with 13 points and 12 boards for TTT Riga, with Russian center Elizaveta Kityzina also scoring 13 in defeat.
Fenerbahce trail undefeated CSKA Moscow by two games.