Barcelona struggled to find its rhythm, and was playing with nearly the same starting line-up that lost to Roma, likely seeking a form of redemption -- and they got what they were asked for.
Luis Suarez netted the first goal 15 minutes into the game, seizing on Philippe Coutinho's pass.
The goal, however, did not affect Valencia's spirit, as the visitors continued to threaten Barcelona's goal, but without making good on any of their opportunities, thanks in part to ter Stegen.
Valencia forward Rodrigo Moreno Machado, known simply as Rodrigo, squandered an opportunity to draw level on a counterattack just minutes into the second half.
Barcelona's advantage was secured after a header from Samuel Umtiti found the back of the net.
Lionel Messi and Coutinho unsuccessfully tried to increase Barcelona's lead, while Andres Iniesta's shot was blocked by Valencia's net minder Neto.
Despite dominating the game, Barcelona substitute Ousmane Dembele downed Jose Luis Gaya inside the area, prompting the referee to award Valencia a penalty with four minutes to go before the second-half stoppage time.
Daniel Parejo successfully converted the penalty, boosting Valencia's spirits.
Valencia could well have conceded a third goal if Neto had not prevailed over Denis Suarez in a one-on-one situation.
With the win, Barcelona extends its undefeated La Liga run, having not lost a match in the Spanish league since April 8, 2017.
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