After a goalless first half in which Heung-Min Son missed a sitter and Hugo Lloris saved a Ramadel Falcao penalty, Monaco and Tottenham decided to start scoring in a frenzied opening ten minutes of the second period.
First Djibril Sidibe headed in to give the hosts the lead four minutes into the second half.
Spurs replied quickly through a Harry Kane penalty after Dele Alli was hauled down in the box.
But Monaco scored again within a minute to re-take the lead — Thomas Lemar scoring his second goal in two appearances against Tottenham.