Balazs Dzsudzsak scored twice as PSV moved to within a point of FC Twente at the top of the league.
The Hungary striker struck in the 25th minute to give his side the lead, before slotting home from the spot 15 minutes from the end after Jacob Lensky had been dismissed for the hosts.
PSV actually played longer with 10 men having had Jonathan Reis dismissed just 33 minutes in, but they held on to the win despite Frank Demounge's consolation.
Utrecht started well and Barry Maguire tested Andreas Isaksson with a low, early drive.
They did not take their early chances, though, as PSV moved in front in controversial circumstances.
The home side felt they should have been awarded a free-kick that was not given and PSV took full advantage by opening the scoring when Dzsudzsak pounced from six yards after Michel Vorm could only parry Ola Toivonen's hit.
Reis saw red eight minutes later when he caught Alje Schut as the pair challenged for a high ball, although a yellow card may have been a fairer outcome.
Schut did his best to give his side a route back after the break with a powerful drive, before Lensky followed Reis down the tunnel after a badly-timed challenge on Toivonen.
That allowed Dzsudzsak to slot home from the spot via the post, and the abuse the referee was receiving in the aftermath almost caused the game to be stopped.
As it was play continued and Demounge slammed home a bicycle kick with nine minutes to go, before Dries Mertens missed a fine chance to level in injury time when he shot straight at Isaksson.