Derk Boerrigter scored the winner for the visitors with 13 minutes remaining after Jeremain Lens had twice pulled PSV level.
Ajax have 66 points with four matches remaining, five ahead of Vitesse Arnhem, who gave away a three-goal lead to draw 3-3 at Roda JC Kerkrade on Saturday.
PSV are a further point adrift in third, ahead on goal difference of Feyenoord, who were held to a 1-1 draw by RKC Waalwijk on Sunday.
In-form Ajax dominated the match and went ahead through Kolbeinn Sighthorsson, who finished from close range after 33 minutes after being set up by Mark van Bommel
A toothless PSV equalised two minutes before the interval when Kevin Strootman punished some sloppy play from Christian Eriksen to tee up Lens for his first.
It was Eriksen, however, who restored the lead early in the second half, making the most of a disorganised PSV defence to cut in from the left and beat defender Timothy Derijck through his legs at the near post.
Lens grabbed his second after 69 minutes, netting a rebound after a free kick from Dries Mertens hit the post, before Boerrigter settled the match, pouncing on a mistake from Erik Pieters to finish.
"We deserved this win although both teams started anxiously but we improved that after the break," Ajax manager Frank de Boer told reporters.
"At 2-1 they were beaten, but our own sloppiness let them back in the match.
"We knew that a win here would be a big step towards the title, having received two presents from (Vitesse and Feyenoord) who dropped points."
Feyenoord went ahead when Italian Graziano Pelle converted a 13th-minute penalty in a match that pitted his coach Ronald Koeman ahead against his brother Erwin in the dug-out.
Sander Duits equalised for Waalwijk ten minutes into a lacklustre second half as Feyenoord lost ground in their bid to win a first title since 1999.
U.S. international Jozy Altidore scored a nine-minute, first-half hat-trick that included two penalties, to inspire AZ Alkmaar to a 6-0 rout at home to nine-man Utrecht.
The visitors had Anouar Kali and Jan Wuytens sent off in the first half.