Cadiz scored twice through Anthony Lozano and Alfonso Espino, before Santi Mina scored Celta Vigos only goal in the second half.
Cadiz raised his score to 5 points in 11th place, after achieving his first victory this season.
Meanwhile, Celta Vigos balance froze at a single point in 18th place, as the taste of victory has not yet been known.
Celtas latest victory goes back to last season when they beat Barcelona at the Camp Nou on May 16.
As for Cadiz, it achieved its first victory since its victory over Huesca on May 8.
Cadiz stopped his bad series at Balaidos Stadium in the Spanish Premier League with 6 defeats.
Cadiz achieved his first victory in La Liga at Balaidos Stadium since March 1986, and his second overall.
Cadiz also defeated Celta Vigo for the first time since May 1990.
Cadiz took the lead with a Honduran header, Choco Lozano, in the 38th minute, after a cross by Chilean Tomas Alcaraz.
Lozano continued to shine, receiving a penalty kick in the 43rd minute after he was fouled by Jose Fontan, Celta defender.
Salvi Sanchez took the lead and missed a save by Argentine goalkeeper Matias Detoro, but Uruguayan Pacha Espino was in the right place to follow the ball past Celta, scoring his second goal of the season.
This will be the second penalty kick that Detoro has saved this season, after he saved another against Osasuna.
At half-time, Celta coach Eduardo Codet made 3 changes at once and sent all his attacking elements onto the pitch.
He pushed Nolito, Brice Mendes and Thiago Galliardo, instead of Fontaine, Denis Suarez, and Franco Cervey.
The changes caused the match to be reversed, in the direction of Jeremiah Ledesma goalkeeper Cadiz in full.
The 64th minute witnessed Celtas first goal by Mina, who followed up on Ledesmas excellent save from Iago Aspas’ shot.
Mina came back in the 73rd minute and missed a confirmed goal with a header that went just short of the goal.
Celtas attacks became fiercer in the last moments, especially when Aspas hit the Cadiz crossbar in the second minute of overtime.
Excitement escalated when Colombian Jason Moreau headed in the sixth minute of stoppage time, but it also bounced off the crossbar.