Phillip Cocu's men had the better of three first-half goals in Arnhem to seal a sixth away league win of the campaign.
The visitors took the lead after seven minutes through Jurgen Locadia, who slotted into an empty net after Vitesse goalkeeper Piet Velthuizen had failed to clear from a backpass.
Vitesse levelled 11 minutes later as Zakaria Labyad found the net with a superb curling effort from the edge of the area.
But PSV clinched the points just prior to the half-hour mark, Memphis Depay seeing his penalty saved by Velthuizen only to nod home from Park Ji-sung's cross after the South Korean had reacted quickest to the rebound.
Elsewhere, Den Haag boosted their survival hopes with a 2-1 home win over 10-man Groningen.
The hosts took the lead 63 minutes in when midfielder Roland Alberg converted from the penalty spot after being brought down by Groningen defender Eric Botteghin, who was sent off despite his foul appearing to take place outside the box.
Groningen levelled 15 minutes later to make light of their numerical disadvantage, Richairo Zivkovic slamming home from Filip Kostic's pass.
But there was to be one final twist, as Den Haag's Dion Malone slotted home a cool finish in the 89th minute to move Henk Fraser's men clear of the relegation play-off places.
In the other game on Saturday, Bryan Linssen took his tally for the season to 13 with a double as Heracles ended a five-game winless league run with a 2-1 success against Roda JC.
