The Basque side benefitted from playing the first game of the weekend to move up from sixth to first. Tomas Pina tapped home Victor Laguardia’s cross for the game’s only goal.
Sevilla drop off top but will overtake Alaves if they beat Barcelona on Saturday (19:45 BST), with the champions also knowing a win would put them top.
Real Madrid can rise to top spot before then as they host Levante at 12:00 BST, with Atletico Madrid and Espanyol also within three points of the new leaders.
Alaves, managed by Abelardo, have never won a major trophy. They lost in the 2001 Uefa Cup final to Liverpool and 2017 Copa del Rey final to Barcelona, and were in the third tier as recently as 2013.
