Real Madrid suffered their ninth La Liga loss of the season and their first under the returning Zinedine Zidane after being outclassed by Valencia.
They have now lost as many league matches this term as in their previous two campaigns combined.
Goncalo Guedes side-footed in a finish for the hosts in the first half and Ezequiel Garay headed in the second.
Karim Benzema pulled a goal back in injury-time for Real, but there was no time remaining to claim a point.