The Eredivisie teams were contesting the first leg of their play-off at the Mandemakers Stadium.
Wilfried Bony's second-half brace put his side in control of the tie ahead of Sunday's second leg at the Gelredome, with Krisztian Nemeth having drawn RKC level early in the second half following Tomas Kalas' opener.
Bony carved out the first chance of the match, forcing RKC goalkeeper Jeroen Zoet to tip over his third-minute shot from the edge of the area.
Zoet had to be alert to push a free-kick wide from Jan-Arie van der Heijden in the 19th minute and following the resultant corner Guram Kashia's shot struck a post as the Vitesse pressure mounted.
It finally told in the 22nd minute as Kalas' long-range strike following another corner gave Zoet no chance.
RKC needed a positive start to the second half and they got it when Nemeth headed home a right-wing cross from fellow substitute Furkin Alakmak 10 minutes in.
Vitesse goalkeeper Piet Velthuizen then kept his side on level terms by keeping out Cuco Martina's header from a Sander Duits cross, and it proved a vital intervention as Bony restored the visitors' lead in the 69th minute.
Kalas' pass did not reach Bony but the forward seized on an error by Martina to bear down on goal and beat Zoet in the one-on-one duel.
Zoet then kept out an overhead kick by Bony, but the Ivorian made it 3-1 with nine minutes to go when he headed home a cross from the left.
Ricky ten Voorde wasted a glorious chance to pull one back, shooting straight at Velthuizen in the 86th minute.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.