The referee took both teams off the field after fireworks were thrown and one enraged home fan ran on to the pitch.
Brazilian teenager Piazon converted the first penalty in the 35th minute after Eagles defender Deniz Turuc was sent off for a foul.
Piazon then had to wait for the teams to return after the stoppage to convert the second spot kick in the 41st minute.
Gael Kakuta, on loan from Chelsea like Piazon, made it 3-0 in the 65th minute to give Vitesse 27 points from 14 games.
Quincy Promes struck twice as Twente Enschede's 5-2 home win over NAC Breda lifted them into third place on 24 points, one behind Ajax and above AZ Alkmaar on goal difference.
Second from bottom RKC Waalwijk's coach Erwin Koeman put one over his brother Ronald with a 1-0 home win over Feyenoord.
"I'm furious and really disappointed," said Feyenoord boss Ronald.
Utrecht moved up to 12th with a 3-0 victory over ADO Den Haag.
(Reporting by Mark Gleeson; editing by Tony Jimenez)
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