Jacob Mulenga fired in-form Utrecht into a 10th-minute lead but the leaders were on level terms again on the half-hour through Belgian forward Dries Mertens.
Georgino Wijnaldum sent PSV ahead on 65 minutes and despite Atiba Hutchinson's red card moments later, they held on.
Ajax can close the gap again when they travel to RKC Waalwijk on Sunday, but FC Twente lost further ground as their recent woes continued with a 1-1 home draw against bottom team Willem II.
Coach Steve McClaren admitted on Friday that his team desperately needed to arrest a poor run that has seen them fail to record a league win since the turn of the year.
But Ricardo Ippel's stoppage-time strike prevented them from doing that after Douglas had headed the opener from close range on 43 minutes.
A stunning Willy Overtoom goal was not enough for AZ Alkmaar as they drew 2-2 at struggling Roda JC.
Roda raced ahead in the first minute through Sanharib Malki but, after Jozy Altidore (34) equalised, Overtoom (51) produced a brilliant 25-yard free-kick to fire AZ ahead.
Their lead lasted just 13 minutes, though, as Frank Demouge ensured Roda inched two points clear of danger.
Finally, NAC Breda and Heracles Almelo shared a 1-1 draw after Rick Ten Voorde (56) cancelled out an 11th-minute opener from Everton.