Quique Setien needed three games in charge of Barcelona to lose his first match as Valencia beat the defending Spanish La Liga champions 2-0.
Valencia striker Maxi Gomez scored once and played a key role in producing an own-goal but also missed a penalty kick on Saturday.
Barcelona hardly threatened to score in the first half at Mestalla Stadium and only got shots on goal from Lionel Messi when already behind.
Barcelona's first defeat in 10 rounds means they will lose the league lead if Real Madrid take a point or more at Valladolid on Sunday. Barcelona lead Madrid on goal difference.
Valencia went ahead through an own-goal by Jordi Alba in the 48th minute. Gomez's volley was going wide but it deflected off the Barcelona left back and went into the net.
Gomez made it 2-0 in the 77th, making up for his missed spot kick in the first half.
It was host Valencia's first victory over Barcelona in 13 consecutive visits by the Catalan powerhouse.
Setien was brought in at the start of last week to replace Ernesto Valverde. The club wanted to give a boost to Barcelona's attack which many believed had strayed from their traditional high-possession passing game under Valverde.
Valencia, however, were content to let Barcelona dominate possession and seek to hit on the break.
"We didn't play well in the first half," Setien said.
"We were not in the right positions in some areas and did not understand what Valencia was doing. We made passes just to make them, but they didn't gain us any advantages."
Raul de Tomas scored in his third consecutive match since joining Espanyol in the winter transfer market in a 1-1 draw with Athletic Bilbao.
Bilbao forward Inaki Williams said he was a victim of racial abuse from fans during the match.
Espanyol moved out of last place but remained winless in all 11 league matches played at home this season.