The visitors had been hoping to keep the pressure on pacesetters Ajax but fell behind after just 10 minutes when 17-year-old forward Richairo Zivkovic showed excellent composure to beat the goalkeeper and find the net, five days after agreeing a deal to join the league leaders at the end of the season.
Chelsea-owned winger Christian Atsu levelled just before the break, but Groningen retook the lead 11 minutes into the second half thanks to Nick van der Velden's strike.
And the home side wrapped up the win with 27 minutes to go as Tjarron Chery scored his sixth Eredivisie goal of the season, keeping Groningen ninth, while Vitesse remain seven points behind leaders Ajax, who are next in league action against Twente on March 30.
PSV Eindhoven's recent resurgence continued in Saturday's late match as they beat Roda 3-1 to keep their UEFA Champions League qualification ambitions alive.
Mitchell Paulissen cancelled out Jurgen Locadia's 14th-minute opener just prior to half-time, but the hosts came back strongly in the second half and sealed the victory thanks to goals from Bryan Ruiz and Jeffrey Bruma.
The victory sees PSV move up to second after an eighth consecutive league win, while Roda remain rooted to the bottom of the table.
Meanwhile, relegation-threatened NEC staged a late comeback to earn a 2-2 draw at Heerenveen.
Bilal Basacikoglu gave the hosts a 40th-minute lead with a superb solo goal, before the prolific Alfred Finnbogason scored from the penalty spot on the stroke of half-time.
NEC fought back, however and after English midfielder Michael Higdon netted 12 minutes from time they equalised through Soren Rieks, despite the sending off of Rens van Eijden for a second yellow card.
