Phillip Cocu's side were beaten at Feyenoord in their last game before the international break, but responded in emphatic fashion in Enschede on Saturday to move a step closer to winning the title.
Luuk de Jong opened the scoring just before the half-hour mark, then further goals from Jeffrey Bruma and Georginio Wijnaldum put the leaders in complete command at half-time.
Depay added insult to injury with two goals in the space of three minutes to take his tally to 25 goals in all competitions, as Twente suffered their first defeat since February.
Ajax will aim to reduce PSV's advantage at the summit back to eight points when they travel to Utrecht on Sunday, but Cocu's men look destined to be crowned champions on the evidence of this display.
Bottom side Dordrecht look doomed after they squandered a lead to lose 3-2 at home to fellow strugglers Heracles.
Goals from Everon Pisas and Joris van Overeem put Dordrect in front at half-time after Bryan Linssen had opened the scoring eight minutes in.
Wout Weghorst equalised 19 minutes from time and Linssen struck again with four minutes remaining to push Dordrecht closer to the drop and move John Stegeman's men two points clear of third-bottom NAC Breda.
NAC enhanced their chances of getting out of trouble by stretching their unbeaten run to three games with a goalless draw at third-placed Heerenveen.
An unfortunate own goal from goalkeeper Sergio Padt ensured Groningen had to settle for a 1-1 draw at Vitesse, while Bram van Polen's first goal of the season ensured Zwolle beat Willem II 1-0.
