Led by coach Roberto Iniguez, the boss who steered Ros Casares to the title last season, Fener pulled away late in the fourth quarter for a 73-48 victory in Group B.
Municipal Targoviste travelled to Turkey still smarting from their 76-75 home setback to Beretta Famila Schio.
There was also the sub-plot of Targoviste coach George Dikeoulakos going up against the side he coached to the Turkish championship earlier this year.
Fener began the contest by scoring 14 of the first 16 points in the game.
Targoviste stayed within striking distance and reduced the arrears to 18-12 on a Gabriela Marginean three-point play.
Fener gradually took control of the game.
With less than three minutes to go in the third quarter, they had a 47-27 advantage.
Targoviste closed the gap to 11 on three occasions in the fourth quarter but ran out of steam.
Fener finished the game on a 15-4 run for a 25-point win.
Ivana Matovic's 22 points led the victors.
Roberto Iniguez, Fenerbahce coach:
"I am happy for winning the game but we could do better than that. We had a lot of easy turnovers . We want to play fast but sometimes this proves difficult; we need time and have to work much more. I am also happy with our defense."
Cappie Pondexter, Fenerbahce:
"We are a great team; to win is good. We did some stupid mistakes but in defense we are very good."
George Dikeoulakos, Targoviste coach:
"We need time to become a team. Fenerbahce is a good team. We will work more and more."
Ivanka Matic, Fenerbahce:
"Fenerbahce played a lot better than us tonight. We look forward and think of the next game."