Feyenoord fire four past Graafschap
Ruben Schaken opened the scoring two minutes into the second half when he intercepted a sloppy pass from Ted van de Pavert, sent off 11 minutes later after a professional foul on John Guidetti who converted the penalty to double the lead.
Kelvin Leerdam headed home the third before Guyon Fernandez sealed the win from the penalty spot to keep Feyenoord on track to quickly forget the bad memories of last season.
They finished 10th last term, their lowest position in 21 years, but Koeman looks to have restored a feel-good factor after taking over from Mario Been.
On Saturday, seventh-placed Vitesse Arnhem hit five second-half goals to thrash Roda JC Kerkrade 5-0 while Heerenveen's three forwards scored in a 3-0 win at VVV Venlo.
Luciano Narsingh broke the deadlock 16 minutes before time and Bas Dost doubled the lead to settle the match before Oussama Assaidi added a third.