Feyenoord controlled the match but had to wait until the 39th minute to take the lead against a Vitesse side who were toothless in attack without injured top scorer Wilfried Bony.
Pelle scored from the penalty spot for his 24th goal of the season after Tomas Kalas had handballed and Immers doubled the lead five minutes into the second half, volleying home after a fluent counter attack involving Pelle and Ruben Schaken.
Feyenoord are now level on 63 points with second-place PSV Eindhoven, who were 3-1 winners at AZ Alkmaar on Saturday, and four behind leaders Ajax Amsterdam, who were held to a 1-1 draw by Heerenveen on Friday.
Vitesse drop to fourth with 61 points with only the top two in the Dutch championship going into the Champions League.
"For the first time in weeks we showed that we can play good football and I was pleased by the way we kept going against Vitesse for 90 minutes," Feyenoord manager Ronald Koeman told reporters.
Twente Enschede remain fifth with 55 points after Rasmus Bengtsson and Luc Castaignos scored two goals in two second-half minutes to salvage a 2-2 draw at lowly VVV-Venlo who had gone ahead through Nils Roseler and Uche Nwofor.
Sixth place Utrecht cruised to a 3-0 home win over NAC Breda thanks to goals from Mike van der Hoorn, Jens Toornstra and Edouard Duplan to move up to 54 points and seal a Europa League play-off berth.