Barcelona forward Depay played in Davy Klaassen to put the Dutch in front inside 54 seconds and then added a couple of his own – a brilliant strike and a penalty – before half-time.
Turkey was reduced to 10 men prior to the interval when Caglar Soyuncu was sent off and the Netherlands did not hold back, with Depay heading in from a yard out for his third of the day.
Cengiz Under profited from a defensive mistake to net a consolation, but only after substitutes Guus Til and Donyell Malen had added their names to the scoresheet in an emphatic victory for Louis van Gaal's men.
Turkey had gone unbeaten in its first five games to lead the way at the top of Group G but were behind in Amsterdam within a minute when Klaassen played a one-two with Depay and slotted in off the post.
The pair linked up again as Klaassen flicked a return pass into the path of Depay, who kept his composure to tuck the ball away from Ugurcan Cakir and put the Netherlands well on course for an eighth straight home win.
Turkey found itself three goals down with seven minutes of the first half still to play – Depay dinking the ball down the middle from the penalty spot after Soyuncu tripped Klaassen in the box.
Soyuncu was booked for that challenge and was issued another yellow card eight minutes later for a foul Depay, who completed his first international hat-trick early in the second half.
Feyenoord midfielder Til spun his marker and blasted in his maiden Netherlands goal and fellow substitute Malen rolled a sixth into an empty net, rendering Under's late tap-in nothing but a consolation on a night to forget for Turkey.