Barcelona s Memphis Depay, left, celebrates after scoring his side s second goal during the Spanish La Liga soccer match between FC Barcelona and Valencia at the Camp Nou stadium in Barcelona, Spain, Sunday, Oct. 17, 2021. AP
The struggling Catalan club moved to seventh place, five points behind leader Real Sociedad and with a game in hand.
Barcelona was coming off two defeats before the international break _ 2-0 at Atletico Madrid in the league and 3-0 at Benfica in the Champions League. It had won only once in its last six matches in all competitions.
The loss extended Valencia's winless streak to five matches. It dropped to ninth place in the league.
Jose Luis Gaya opened the scoring for the visitors with a powerful long-range shot five minutes into the match at the Camp Nou Stadium, but Fati equalized from outside the area in the 13th and set up the penalty kick converted by Depay in the 41st.
Coutinho, marred by injuries since returning to Barcelona, sealed the victory from close range in the 85th for his first goal with the Catalan club in nearly a year. American defender Sergino Dest made the pass for the Brazilian.
Dest came off in the final minutes to allow the debut of Sergio Aguero, who was signed by Barcelona from Manchester City for this season but was yet to play as he had been recovering from injury.
Barcelona coach Ronald Koeman was back on the bench after a suspension of two league matches following a red card for complaining.
Barcelona has begun a three-game home stint that Koeman called key to getting the team back on track. It will next play a critical Champions League game against Dynamo Kyiv on Wednesday and then the first ``clasico'' of the season against Real Madrid.
``It was a very important win, we are in a key week in the season,'' Barcelona midfielder Frenkie de Jong said. ``We started it well by earning points and gaining confidence, that's very important for the club right now.''
Barcelona is two points behind Madrid, Sevilla, Osasuna and defending champion Atletico Madrid. Madrid and Atletico had their weekend games postponed because some players were on international duty with their national teams.
Barcelona's delegate members earlier Sunday approved the club's financial accounts for the 2020-21 season with losses of 481 million euros ($557 million). They also gave their approval to a budget of an operating income of 765 million euros ($886 million) for 2021-22.
``We have to look forward and focus on getting the club back to its old self,'' club president Joan Laporta said. ``We have been working tirelessly for six months to get the club out of the institutional pit that it has fallen into. But we are not going to be able to fix this situation overnight.''
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