The outcome has left Randy Wiel's team undefeated at 4-0 and dropped Swans to 0-4.
The game was knotted at 36-36 when the Dutch outfit went on the 10-0 run which lasted two minutes.
Anthony Richardson had six points in that scoring burst.
They opened up a 68-51 lead early in the fourth quarter only for Swans to score 12 consecutive points and trail 68-63 with 4:02 to go.
David Jackson replied with a three for the home side and the Austrian team got no closer than five for the remainder of the contest.
Deteri Mayes had 23 points and Fisher 19 for Swans while Jerome Beasley scored 19 and Richardson 15 for EiffelTowers.
Randy Wiel, EiffelTowers coach:
"We just about managed to do enough to win the game.Offensively it wasn't our best performance, but we showed some good stuff in defense. I don't know how people pick MVPs in games like this, because this was an excellent team performance."
Bob Gonnen, Allianz Swans coach:
"We had double their amount of turnovers. That's the game [lost] right there."
Taron Downey, EiffelTowers player:
"We kept focused mentally. That was good."
Peter Hütter, player Allianz Swans:
"We started well, but couldn't finish it."