Goals from Tom Beugelsdijk and Danny Bakker put Den Haag - bottom before kick-off - 2-0 up at the break, and a first league win in four games seemed assured.
However, a Feyenoord fightback nearly spoiled the celebrations.
Jordy Clasie and Graziano Pelle brought Ronald Koeman's side level with 16 minutes to play, but Roland Alberg's first goal for the club secured the three points and lifted Den Haag out of the bottom three.
Park Ji-Sung's shot was blocked by the AZ defence, but the full-back latched onto the loose ball and fired home his fourth goal of the season from 20 yards after just three minutes.
The win moves Philip Cocu's side into sixth place, above AZ and Groningen, as their campaign continues to recover from a dreadful start.
PEC Zwolle ended a run of nine Eredivisie games without a win with a rousing comeback against NAC Breda, Ron Jans' side scoring twice in the second half to earn a 2-1 success.
Elsewhere, Roda eased their relegation worries with a 1-0 victory over Utrecht in Jon Dahl Tomasson's first home league game in charge.
Utrecht's fall down the table continues, though, as the defeat was their fourth in a row and sees them slip back into the bottom half.
