The hosts headed into Saturday evening's match sitting bottom of the table and seven points from safety after winning just one of their previous 15 matches, most recently going down 6-0 to Girona last weekend.
La Liga's form book was turned on its head, though, as Jonathan Viera and Jonathan Calleri netted to earn the strugglers a comeback win, denying their opponents the chance to move into second place in the process.
Mina almost doubled his tally in the first half, with his next effort striking the crossbar, but that would prove to be a key moment as skipper Viera pounced on a knockdown and thumped the ball into the roof of the net.
Calleri converted to put Valencia on the brink of a first defeat since the winter break, which was effectively confirmed when Vezo joined Gabriel in picking up a second yellow.
The closest Los Che came to a leveller was late on when Simone Zaza swivelled on the edge of the box and dipped a shot just wide of the far post, meaning a rare lifeline for Las Palmas as they climb one place in the table.
LAS PALMAS (4-3-3): Chichizola; Navarro, Galvez, Lemos (Simon 46'), Castellano; Tana, Penalba (Castellano 80'), Viera; Toledo, Samperio (Halilovic 76'); Calleri
VALENCIA (4-4-2): Neto; Montoya, Paulista, Vezo, Latorre; Maksimovic, Coquelin, Kondogbia, Gil; Mina (Zaza 74'), Rodrigo (Vietto 68')