Peter Bosz's men took just one point from their first four games at the start of the season, but have since turned things around and continued that revival in fine style on Friday.
Two goals in the first 14 minutes from midfielder Kelvin Leerdam put the hosts in command at the GelreDome in Arnhem.
Leerdam burst into the box and opened the scoring with a powerful drive beyond Den Haag goalkeeper Martin Hansen, who he then beat again by cleverly flicking home Abiola Dauda's right-wing cross.
Attacker Michael Kramer pulled one back for struggling Den Haag in the 21st minute, but Vitesse responded superbly and made the game safe before half-time.
First. Den Haag defender Timothy Derijck headed into own net in the 31st minute before midfielder Vejinovic effectively sealed the points six minutes later with a deflected free-kick.
Vejinovic added his second from the spot five minutes before the interval after Mike van Duinen was ruled to have handled in the area.
And the 24-year-old completed his treble with a second penalty in the 62nd minute following Kevin Jansen's foul on Dauda.
The result sees Vitesse surge to ninth in the Dutch top flight while Den Haag are 15th.
