The hosts came from behind in the second half to beat their opponents to earn the coach his first win in the league and lift the team up to 12th in the table
Gary Neville oversaw a La Liga victory for the first time in 10 attempts as Valencia came from behind to defeat Espanyol 2-1 at Mestalla on Saturday.
The Englishman's future has been under heavy scrutiny after his struggles in the league were followed by a 7-0 defeat at Barcelona in the first leg of his side's Copa del Rey semi-final this month.
Neville had conceded that the contest against struggling Espanyol, who had lost their previous two league games 6-0 and 5-0, was a must-win game.
It looked like Valencia were set for another miserable day when Oscar Duarte headed in from close-range after Burgui's corner on 52 minutes.
But the home side levelled in the 71st minute when Joao Cancelo's impressive run enabled Alvaro Negredo to find the bottom corner via a deflection.
The comeback was complete five minutes later when January signing Denis Cheryshev powered home a header from Sofiane Feghouli's cross.
Goalkeeper Diego Alves made a superb reflex stop from Alvaro Gonzalez late on and Neville's heart would have been in his mouth again when Gerard Moreno struck inches wide in the last minute as Valencia survived.
- Goal