Ronald Koeman's side finished third last season but had not picked up any points in three games.
Pelle opened the scoring after 38 minutes before pouncing again 60 seconds later to give the hosts a 2-0 half-time lead.
The Italian rounded off the scoring for Feyenoord nine minutes after the break and, although Joey Suk pulled one back after an hour, it made no difference to the final outcome.
Vitesse Arnhem claimed their first win of the season with Mike Havenaar's solitary goal halfway through the first half proving enough to secure a 1-0 victory over FC Twente.
FC Utrecht also secured their first victory of the season, downing AZ Alkmaar 2-0, as Steve De Ridder scored both goals after 54 and 66 minutes.
FC Groningen managed to scramble a 3-3 draw against Go Ahead Eagles with a late equaliser from Genero Zeefuik despite being reduced to nine men.
Go Ahead Eagles went ahead after 11 minutes through Marnix Kolder before Tjaronn Cherry levelled in first-half injury-time.
Kolder restored the lead three minutes after the break only for Krisztian Adorjan to draw Groningen level.
However, the hosts regained the lead through Xandro Schenk with a little more than half an hour remaining and their task appeared easier when Adorjan was sent off after 68 minutes.
He was followed down the tunnel just two minutes later by team-mate Timo Letschert but it did not derail the visitors who found the vital equaliser with three minutes remaining.