Monaco - Striker Cenk Tosun scored twice as Besiktas won 2-1 away at Monaco for a third straight win to move closer to qualifying for the Champions League knockout stage on Tuesday.
Monaco, last season's swashbuckling semi-finalists, are heading the other way with one point from three matches.
However, with Liepzig beating Porto 3-2 in Group G's other game, Monaco still have a chance and play Besiktas away on November 1.
With three games left, Liepzig have four points and Porto three.
"It was a balanced game, competitive from both sides. The difference was that they were more efficient," Monaco coach Leonardo Jardim said. "They were more mature in the key moments. But the attitude and hard work of our players is the path to follow, and they gave their all."
Still, Jardim may have to look at himself first of all.
He made the odd decision in a must-win game of leaving attacking midfielder Rony Lopes on the bench - even though Lopes has been one of the team's best players and scored a fine goal last Friday in a league game against Lyon.
Radamel Falcao put Monaco ahead in the 30th minute after running onto Balde Keita's well-timed pass and guiding the ball into the right corner. It was the Colombia striker's 13th goal of the season.
Monaco's lead lasted three minutes, as weak defending allowed veteran right winger Ricardo Quaresma space to ping an accurate cross that Tosun met with a close-range header for the Turkish visitors.
Last week, Tosun scored twice for Turkey against Finland in a World Cup qualifier. Last season, he netted 20 league goals for the Istanbul side.
Tosun showed those poaching instincts, finishing neatly after midfielder Tolgay Arslan's shot came back off the post in the 54th.
Monaco scored more than 150 goals in all competitions last season, winning the league in style and falling to Italian champion Juventus in the Champions League semi-finals.
But this side has none of the same verve after key players were sold in the off-season.
Winger Ryan Babel had an early goal ruled out for offside for Besiktas, with television replays showing he was level with the defender.
Veteran defender Pepe was lucky to avoid a red card as the last man after hauling down striker Keita Blade, and from the free kick goalkeeper Fabri punched away Thomas Lemar's effort.
It was a rare Monaco chance.
Moments later, Monaco goalkeeper Danijel Subasic kept out Atiba Hutchinson's volley.