The win is a vital one for the Turkish giants, who climbed into second place and will next week try to win for the seventh time in Group D when they host Italian strugglers Beretta Famila.
The game was knotted at 50-50 with 2:36 to go in the third quarter when Ajavon buried a three-pointer for Fener and put them in front for good.
Turkey international center Nevriye Yilmaz followed with a basket to leave the visitors with a 55-50 lead heading into the final frame.
Emilie Gomis took the run to seven points with a lay-up at the start of the fourth quarter and the French got no closer than three points for the remainder of the contest.
Sheana Mosch had 23 points for Lattes Montpellier.