Piazon opened the scoring with a 35th-minute penalty after Deniz Turuc had brought down Mike Havenaar inside the area, with the home midfielder earning a straight red card for the foul.
Brazilian teenager Piazon then made it 2-0 with another penalty just before half-time following a handball by former Vitesse defender Jop van der Linden.
The visitors introduced Kakuta at the break and the French winger added a third in the 65th minute as Vitesse moved back to the top of the table back above Ajax, who beat Heracles on Saturday.
Twente are third, a point behind Ajax, after beating NAC Breda 5-2.
Kyle Ebecilio, Dusan Tadic, Luc Castaigno and Quincy Promes were on the mark for Twente, with NAC's replies coming from Kenny van der Weg and Danny Verbeek.
Groningen slipped to fifth after being held goalless at home by PEC Zwolle, whose point saw them climb to sixth above Feyenoord after the Rotterdam outfit slumped to a 1-0 shock defeat at RKC.
RKC had only picked up two wins and nine points from their opening 13 matches but a last-gasp winner from Aurelien Joachim saw them upset Feyenoord.
In Sunday's other Eredivisie match, FC Utrecht beat ADO Den Haag 3-0 with goals from Steve De Ridder, Yassine Ayoub and Kai Heerings..
Utrecht lost Mark Van der Maarel to a red card 15 minutes from time but had already wrapped up the points by then.