It was the third consecutive victory for Odense, who are second in Group B with 11 points after seven matches. Brest tops the table with one more point for one match less.
The two best teams are guaranteed a place in the quarter-finals, while the third to sixth teams will have to go into knockout matches to reach the same stage.
Right from the start of the match, Odense took the lead and quickly took an 8-4 lead thanks to winger Elma Halilcevic.
Odense dominated the game, scored almost at will, and opened up a nine-goal gap at 19-10 thanks to the Spanish profile Lysa Tchaptchet.
Krim managed to reduce the deficit a couple of times before the break, but Odense went into the interval with a 23-16 lead.
The Danish lead was extended midway through the second half, when Odense led by 11 goals several times, and Krim never came close to getting back into the match.
However, the Slovenians managed to improve the cosmetics of the scoreboard slightly towards the end as three successive goals saw them lose by eight goals.