The Rotterdam club had lost their opening three league matches and a Europa League tie in Russia on Thursday, but bounced back with the flamboyant Italian scoring twice in two minutes in the first half and completing his treble in the 53rd.
Feyenoord started slowly in a tense atmosphere at Rotterdam's De Kuip stadium but once Pelle had got his head to a Jordy Clasie free kick to open the scoring, the mood lifted dramatically and the team were rarely troubled on their way to victory.
"We needed that," coach Ronald Koeman told Dutch television after the match. "When you don't have any points out of a possible nine, then you have to accept there is pressure."
Relief for Feyenoord was matched in Utrecht where Belgian Steve de Ridder netted both goals as the home side also posted their first win of the season by beating AZ Alkmaar 2-0.
Japan international Mike Havenaar scored the only goal with a first half header as Vitesse Arnhem beat Twente Enschede to join their opponents and another four clubs on seven points, five behind early leaders PEC Zwolle.
Marnix Kolder twice scored for promoted Go Ahead Eagles but they were held to a 3-3 draw by Groningen, who ensured an away point with a 87th equaliser from substitute Genero Zeefuik.