Zaragoza dominated on the glass, out-rebounding the hosts 44-29.
They were also a scintillating 33 of 48 (68.7%) from inside the arc compared to LMK's 21 of 55 (38.1%).
Mann Filter never trailed in this game and took control for good with a 12-0 run midway through the opening quarter for a 20-6 lead.
Early in the second frame and the lead had ballooned to 30-10.
Agne Ciudariene had 14 points and nine rebounds for the winners.
Ciudariene scored eight points in the first nine minutes to help the Spanish outfit claim a 22-8 advantage.
Florina Diacona and Ildiko Vass each scored 17 points in defeat.
The second leg will be played in Spain on January 14.