Giresunspor were awarded a penalty kick when Besiktas's right back Valentin Rosier handballed in the area.
Malian winger Fousseni Diabate scored from the white spot in the 21st minute in Istanbul's Vodafone Park.
In the 39th minute, Besiktas defender Necip Uysal was sent off after a harsh tackle against Diabate. The Black Eagles were down to 10 men.
Senegalese forward Ibrahima Balde doubled the lead for Giresunspor in the 54th minute with a long through ball that tricked the Besiktas defense.
Besiktas goalie Mert Gunok left his goal as he was aiming to clear it with a misjudged header in a big mistake that turned into an easy goal for the visitors as Balde followed the ball to score an open goal.
Giresunspor did not stop scoring as they entered the area with several passes. Balde took a low shot, but it was parried by Gunok, while Sergio followed the rebound to score an easy chance in the 64th minute.
Seven minutes later, Rosier curled a cross from the right wing that sent the ball into the bar -- an unexpected effort might have been an interesting goal.
Near the end of the game, Giresunspor made it 4-0 on a quick counter attack. Joe Champness, who was assisted by Flavio, scored an open goal.
Gunok was injured in his knee immediately before Flavio's assist as the Besiktas goalkeeper abruptly tripped himself on the grass. The game went on as Champness finished.
Gunok then left the pitch on a stretcher.
Following the shocking 4-0 loss, last season's Turkish champions Besiktas are now in mid-table with 20 points in 14 matches.
Giresunspor collected 16 points to be in the 13th spot of the standings, while Besiktas are 13 points behind leaders Trabzonspor, who will visit Istanbul's VavaCars Fatih Karagumruk on Sunday.
Week 14 results
Adana Demirspor - Kasimpasa: 0-0
Medipol Basaksehir - Altay: 0-0
Fraport TAV Antalyaspor - Aytemiz Alanyaspor: 3-0
Caykur Rizespor - Yukatel Kayserispor: 1-0
Besiktas - GZT Giresunspor: 0-4
