With 50 points from 25 games, third-placed Feyenoord are three points behind league leaders PSV Eindhoven, who beat VVV Venlo 2-0 on Saturday. Second-placed Ajax Amsterdam have a point more than Feyenoord after Saturday's 2-0 win at Twente Eschede.
Feyenoord opened the scoring after 11 minutes when a superb defence-splitting pass from Tonny Vilhena set up 18-year-old Boetius, who finished with a tight-angled shot.
Italian Graziano Pelle scored his 19th league goal of the season when he headed home a cross from Ruben Schaken three minutes before the break to double their lead and connected with Boetius seven minutes from time to settle the match.
"We played a superior first half and rewarded ourselves with the second goal just before the break," Feyenoord manager Ronald Koeman told reporters.
"And that is quite an achievement from this young team who are playing must-win matches ... if they want to be champions."
Feyenoord, with seven starters coming from their own youth department, last won the title in 1999.
In other action, Dutch Cup finalists AZ Alkmaar slipped to 15th spot following a 2-1 defeat at fellow strugglers RKC Waalwijk. With 25 points, they are above the relegation zone on goal difference only.
Mart Lieder put Waalwijk ahead in the 39th minute but U.S. international Jozy Altidore equalised on 69 minutes with a fine lob after an assist by Adam Maher before Lieder restored the lead seven minutes later with his second.
Lowly Roda JC Kerkrade cruised to a 4-1 home win over Groningen, with Frank Demouge scoring twice, but stayed in the relegation zone with 25 points.