All the goals were scored in the opening 26 minutes, with Mike Havenaar netting what would prove to be the winner after NAC defender Jordy Buijs had cancelled out Zakaria Labyad's eighth-minute opener for the hosts.
The victory is Vitesse's third on the trot and moved them to within five points of Ajax, who face Cambuur on Sunday.
In-form PSV Eindhoven climbed up to fourth, 10 points behind the pacesetters, after Jurgen Locadia's 51st-minute strike earned them a 1-0 win over FC Utrecht - their sixth successive league victory and ninth in their last 11 matches.
The Eredivisie's leading scorer was again on the mark as Alfred Finnbogason notched his 23rd of the season in Heerenveen's 3-0 home win over PEC Zwolle, the Icelandic ace wrapping up the scoring after Bilal Basacikoglu and Rajiv van La Parra had struck for the hosts.
AZ Alkmaar took advantage of the 24th-minute dismissal of Heracles defender Milano Koenders to record a 4-0 victory over the Almelo outfit.
AZ were already leading through Aron Johannsson's strike when Koenders was handed his marching orders, and the hosts made the most of their numerical advantage with further goals from Johannsson (37), Mattias Johansson (79) and Viktor Elm (90).
Saturday's other game spiced up things at the foot of the table as Roda JC ended a six-match losing streak with a 3-1 win over NEC Nijmegen, a result that sees them leap-frog their opponents and off the bottom.
A brace from Guus Hupperts, either side of a 53rd-minute Marc Hocher goal, put Roda in complete control and although NEC pulled a goal back on the hour through Michael Higdon, the visitors could not find an equaliser and ended up with 10 men following Victor Palsson's late dismissal.
Roda's win means there are now just five points covering the bottom eight teams ahead of Sunday's games.