Edison Cavani had given the hosts an early lead in a match that made little difference with the Italians also confirmed as heading through to the knockout stages in the runners-up slot.
Heading into the game on the back of three successive losses and having long since seen their Group F qualification hopes ended, PSV could hardly have travelled to Italy full of confidence.
And unsurprisingly it was the Italians, who in complete contrast came into the match having won three straight, who started best with Bruno Uvini flashing a sixth-minute shot just wide.
Eduardo Vargas and Hugo Campagnaro also came close before the seemingly inevitable opener arrived in the 18th minute when Marco Donadel set up Cavani to slide home the ball from 12 yards.
But Matavz served notice of his intent when he headed just wide three minutes later in the first chance for PSV, and he grabbed the equaliser just before the half-hour when he followed up after a long-range shot by Memphis Depay rebounded off the post.
Cavani could have put Napoli back in front almost immediately, then PSV keeper Boy Waterman was forced to save with his feet to deny Vargas as the Italians responded well to their setback.
But PSV went ahead five minutes before the break when Matavz grabbed his second, again following up from close range after Cristian Maggio's initial effort had been parried by Antonio Rosati.
Andrea Dossena brought a fine save out of Waterman just before the break and Cavani came close early in the second half, but PSV continued to have the better chances with a Depay strike brilliantly tipped over by Rosati.
Matavz completed his hat-trick when he converted a Depay cross on the hour mark, and PSV stood firm in the face of plenty of Napoli pressure to wrap up only their second win of a forgettable group phase.