The visitors' four goals came on just four shots on Monday. Valencia made a good start, forcing Las Palmas back with a high press that led to a goal in the sixth minute by Santi Mini, who headed in a corner kick, reports Efe.
But it didn't take long for the Canary Island side to find the holes in the Valencia defence and the equaliser came in the 15th minute on a header from Marko Livaja.
Las Palmas took the lead in the 24th minute as Jonathan Viera converted from the spot after Cancelo was called for a foul against Dani Castellano.
The visitors' headline signing of the summer, Kevin-Prince Boateng, brought the advantage to 3-1 with a goal in the 31st minute.
Mina clawed one back for Valencia three minutes later and would have completed the hat trick in the second half if Las Palmas goalkeeper Javi Varas hadn't managed to get a hand on the ball at the last second.
Paco Alcacer hit the cross-bar from a distance in the 70th minute, which turned out to be Valencia's final scoring opportunity of the match.
Livaja added an insurance goal for Las Palmas with two minutes left in regulation.