The Brazilian defender Alex took advantage of slack marking to head home Mark van Bommel's eighth-minute corner.
PSV looked composed throughout and Alex was involved at the other end when he tackled Emmanuel Adebayor on the edge of the area in a rare Monaco break.
Andre Ooijer missed an opportunity to double PSV's advantage when he hit a shot high over the bar on 55 minutes.
Monaco manager Didier Deschamps
"It is a disappointing result especially because we didn't score a goal.
"We will leave with mixed feelings because in my opinion this defeat was not necessary but we didn't play well in attack.
"My strikers lost too many battles, although PSV have a good defence full of internationals."
PSV: Gomes, Ooijer, Lee, Alex, Bouma, Van Bommel, Park, Cocu, Vogel, Vennegoor of Hesselink, Farfan (Beasley 52).
Subs Not Used: Zoetebier, Addo, Bogelund, Lucius, De Jong, De Pinho.
Booked: Vogel.
Goals: Alex 8.
Monaco: Roma, Evra, Maicon, Rodriguez, Givet, Plasil, Bernardi, Zikos, Kallon, Saviola, Adebayor (Nonda 82).
Subs Not Used: Audard, Modesto, El Fakiri, Perez, Farnerud, Gigliotti.
Booked: Rodriguez.
Att: 32,000
Ref: Luis Medina Cantalejo (Spain).
MMIX
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