Tottenham slipped to third in their Europa Conference League group and will have to beat Rennes to progress if their postponed fixture is rearranged.
Thomas Buitink, Daan Huisman and Lois Openda scored as Vitesse beat NS Mura with Amadej Marosa replying for the visitors.
Antonio Conte's side are three points behind Vitesse in Group G with the same goal difference.
Spurs' match with Rennes was called off after a Covid-19 outbreak at the club.
Uefa says it will look at the issues that led to Tottenham stating that the game would not take place.
European football's governing body must determine the fitness of Tottenham's squad, plus the extent of the health guidance offered before making a ruling. Uefa's rules state that if clubs have 13 fit players on their A list, including a goalkeeper, they must play.
Uefa could order the game to be re-arranged, although with a 31 December deadline for the group stage to be finished, finding an alternative date will not be easy.
With Spurs and Vitesse level on their head-to-head results with away goals abolished, the English side would qualify for the knockout round play-off if their match against Rennes, who have already won the group, takes place and they win.
The draw takes place on Monday and would pair them with one of the third-placed teams from the group stages of the Europa League.