The home side had Anouar Kali sent off after 69 minutes but grabbed the lead three minutes later when Dave Bulthuis scored following a corner.
Utrecht were reduced to nine men when Alexander Gerndt was dismissed with 10 minutes but PSV could not capitalise.
On a bad day for the Eindhoven side, midfielder Mark van Bommel picked up a fifth successive yellow card and will be suspended for next week's clash against Feyenoord.
United States international Jozy Altidore's hat-trick inspired AZ Alkmaar to a 4-0 home win over Roda JC Kerkrade.
Altidore opened the scoring after 13 minutes with a fierce finish and sealed the win five minutes before the interval with his second after he had set up Kevin Falkenburg to double the lead.
The 22-year-old completed his hat-trick after the break, taking his tally for the season to seven.
Twente Enschede, 6-2 winners over Willem II Tilburg on Saturday, are top with 15 points after five matches, two ahead of Vitesse Arnhem, who registered their fourth straight win by beating Groningen 3-0.
Vitesse were reduced to 10 men after 30 minutes when Jan-Arie van der Heijden was sent off but in the second half Japan international Mike Havenaar headed home the opening goal before Tomas Kalas and Wilfred Bony added two more in the final minutes.