Ajax recovered from a goal behind to win the match regarded as the Dutch league season's 'classic' to claim a second win in three matches this new season.
Defeat plunges Feyenoord into crisis after a third successive loss - their worst ever start to a season.
Italian import Graziano Pelle put Feyenoord ahead after six minutes despite the expected frenetic start by Ajax in the
Amsterdam Arena but the lead lasted only until the half hour mark when Ruud Vormer brought down Viktor Fischer and Iceland international Sigthorsson converted the resultant spot kick.
Sigthorsson, beginning to feature regularly after a long series of injuries, put Ajax ahead six minutes later with a shot that went in off the underside of crossbar.
Danish teenager Fischer might have made it 3-1 before the break but he hit the post.
Pelle had the best chance of a poor second half as Ajax held on to stretch to 10 matches their unbeaten run against their Rotterdam rivals.
PSV Eindhoven and PEC Zwolle are the early season leaders in the Dutch league with a 100 percent starts after wins on Saturday.