Netherlands international De Jong scored twice inside eight minutes to put PSV in control at the AFAS Stadion, only for goals either side of half-time from Markus Henriksen and Robert Muhren to pull the fourth-placed hosts level.
However, a quickfire double from Georginio Wijnaldum and De Jong earned the points for Phillip Cocu's side - who celebrated a 10th straight league victory.
PSV came flying out the blocks and took the lead in the third minute when De Jong did well to place his follow-up shot into the bottom right-hand corner after Esteban Alvarado made a smart stop from Wijnaldum's initial effort.
De Jong was on the scoresheet again five minutes later with a looping header from a Jetro Willems corner, before Memphis Depay thought he had slotted home a third - only to be denied by the offside flag.
Depay almost scored at the wrong end when his defensive header cannoned back off the crossbar, but AZ did have a goal back half-time thanks to a composed finish from Henriksen.
AZ deservedly levelled through Muhren's emphatic near-post finish four minutes after the break, but Wijnaldum put PSV back ahead with a classy side-footed volley - the goal standing despite protests from the hosts of a foul in the build-up.
De Jong completed the win on the hour with a clinical finish from Luciano Narsingh's cross from the right, as PSV moved 15 points clear of second-placed Ajax, who entertain Twente on Sunday.
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