Lionel Messi scored his first league goal since September, but Los Che stole the headlines with an incredible victory.
Gerardo Martino's side got off to a great start as Alexis Sanchez’s seventh-minute effort fortuitously beat Valencia keeper Diego Alves
After they generally dominated the first half, the visitors drew level just before the break. Dani Parejo finished off a move he started to peg Valencia back, and the diminutive Pablo Piatti put Juan Antonio Pizzi's men ahead with a header early in the second half.
Lionel Messi then equalized for Barca from the penalty spot on 54 minutes to end a run of three matches in all competitions without a goal, but Valencia's determination shone through and Paco Alcacer guided Sofiane Feghouli's cross past Victor Valdes five minutes later.
Things went from bad to worse for Barca when Jordi Alba was sent off with 12 minutes to go, and Valencia held out to become the first La Liga side apart from Real Madrid to leave the Camp Nou without a defeat since Sevilla snatched a 0-0 draw in October 2011.
The hosts were without the services of Neymar, who is still sidelined with an ankle injury, while new signings Seydou Keita - a former Barca player - and Vinicius Araujo were not involved for Valencia.
The Camp Nou was hushed in a minute of silence before the match following the death of former Spain coach Luis Aragones, but the hosts were typically businesslike once the game started and it took them just seven minutes to go ahead.
Sanchez collected Messi’s low cross at the back post and the ball looped over Alves after the winger hit his first-time effort into the ground from a tight angle.
Valencia went agonizingly close to drawing level 37 minutes in as Ricardo Costa headed wide of an open goal following Valdes' failed attempt to clear a corner, but the away side's next opportunity was not wasted.
Parejo launched a swift counterattack after stealing possession in the middle, with the former Real Madrid youngster laying the ball off to Sofiane Feghouli before tapping in the Algerian's low cross.
Valencia began the second half in excellent fashion and took an unlikely lead three minutes after the restart. Paco Alcacer flicked on Antonio Barragan's cross and Piatti beat Dani Alves in the air to head beyond Valdes.
Barca was soon level again, however. Costa was adjudged to have handled the ball inside the area and Messi confidently buried the penalty in the top-right corner, but parity only lasted until the 59th minute.
Feghouli charged into the right side of the area before cutting a low cross back into the area and Alcacer stroked a first-time effort past the helpless Valdes.
Alba compounded Barca's misery by picking up a second yellow card in the final 13 minutes and Valencia held out for a famous victory.