Both teams have 34 points from 15 games but Twente, who beat 10-man ADO Den Haag 2-0 on Saturday, stay ahead on goal difference.
PSV Eindhoven, who suffered their second defeat in a row on Saturday, 3-1 at Ajax Amsterdam, slip to third on 33 points while Ajax are fourth on 30, the same as fifth-placed Feyenoord.
Marco van Ginkel put Vitesse ahead with a fierce drive from 17 metres after 10 minutes and three minutes before the break a fine pass from the league's top scorer Wilfried Bony allowed Reis a free run to double the lead.
Reis settled the match after 62 minutes, netting the rebound after a volley from Bony, who has scored 15 league goals this season, hit the bar.
A brilliant volley from Jacob Mulenga seven minutes from time earned Utrecht a 2-1 win over AZ Alkmaar to stay sixth on 25 points.
Leon de Kogel had put Utrecht in front after 48 minutes before Alkmaar equalised two minutes later through Etienne Reijnen.
Melvin Platje rescued a 1-1 draw for NEC Nijmegen nine minutes from time at home to lowly NAC Breda after the visitors had taken the lead on 59 minutes through Anthony Lurling.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.