Tottenham said this week it couldn't play Thursday as scheduled because of its COVID-19 outbreak that also forced the postponement of the team's Premier League match at Brighton on Sunday.
Conte seemed to have already given Tottenham a much-needed spark as his team led 3-0 after just 28 minutes, but Vitesse pulled two goals back before halftime.
Meanwhile, West Ham United head to Belgium to play Genk with a chance of securing their place in the knockout stage with two games to spare in Group H.
Kane, yet to score in the league this season, completed his treble in the closing minutes after a slick pass from Lo Celso.
Roma are Italy's representatives and Jose Mourinho's side came from behind to thump CSKA Sofia 5-1.
Nicolo Zaniolo and substitute Stephan El Shaarawy both scored in the second half as Roma progressed with the minimum of fuss.
England striker Kane had wanted to leave Spurs in the close season for Manchester City, but was denied a move by club chairman Daniel Levy.
Coach Nuno Espirito Santo made 11 changes to the team that defeated champions Manchester City in their Premier League opener at the weekend.
Two penalties from Franck Kessie helped Milan to a 2-0 win at Atalanta, which had already claimed a top-four spot along with Serie A champion Inter Milan.