Freiburg couldn't build on their win in the Conference League season opener and were beaten 3-0 at Monaco on Thursday.
Last season's Europa League runners-up started this term with a 3-2 win against Jablonec, but failed to repeat their success.
The hosts took the lead shortly before the break after collecting Mio Backhaus' careless ball reposition. Paris Brunner then flicked the ball over Max Rosenfelder before going on a run and slotting it home.
It took them a while, but Monaco were again on target in the 83rd. Ansu Fati's shot was well saved by Backhaus, but the rebound fell to Lamine Camara, who fired it home.
Fati got one himself in stoppage-time, lashing home into the bottom corner and completing the big win.
Freiburg will have to move one quickly as they have a Bundesliga table-topper against league leaders Bayern Munich on Sunday.