Striker Borja Baston pulled the 2001 UEFA Cup runners-up level in the 21st with a scrappy, deflected shot from inside the area, while midfielder Tomas Pina put Alaves ahead in first-half stoppage time after a period of heavy pressure.
The win took Alaves to 31 points from 18 games, one ahead of European champions Real Madrid who host Real Sociedad on Sunday, and saw the Basques reach their highest points total in the first half of a La Liga season.
"It's unbelievable that we have got to 31 points at this stage and our performance today was also unbelievable," said Alaves coach Abelardo Fernandez, who inherited a side struggling for La Liga survival when he took charge 13 months ago.
"We played so well in such difficult conditions, on an icy pitch and against a team like Valencia who gave everything. I'm so grateful to our players and our supporters."
Valencia, who finished fourth last year, are 11th on 22 points after a defeat that will pile more pressure on coach Marcelino, who last month faced calls from fans to be sacked.
"What happened today has a difficult and simple explanation," Marcelino said.
"We started well on a pitch that was impractical and that was half frozen. Then we conceded two goals from set plays, their biggest weapon, both of which were avoidable."
(Reporting by Richard Martin; Editing by Ken Ferris and Pritha Sarkar)
