Luis Suarez and Samuel Umtiti were on target for Barca, who had to endure a nervous final few minutes after Daniel Parejo converted a late penalty for Valencia.
The win at the Camp Nou, which was more comfortable than the scoreline suggested, also eases fears that Tuesday's Champions League collapse against Roma could affect Barcelona's march to the league title.
Ernesto Valverde's side lead their nearest challenger, Atlético Madrid, by 14 points, with Diego Simeone's team hosting Levante and fourth-placed Real Madrid visiting bottom-placed club Málaga on Sunday.
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"They have the most points there, they average three goals per game and have conceded just seven".
"The week has been hard and that hard week affects everyone, including the fans".
"We've tried to confirm the great league season we're having after the blow of the other day. You want to repay them".
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The Reds took the lead on seven minutes when Sadio Mane's initial header was saved well by Asmir Begovic but the forward slammed home the rebound.
Here, Sports Mole looks at the Argentina international's record in past encounters with this weekend's opponents.
"We are going there with ambition, but what happened in the Champions League surely won't leave any negative repercussions". Ivan Rakitic was replaced in midfield by Paulinho while Philippe Coutinho came in for Nelson Semedo.
That seemed to spur on the hosts as they went ahead after 15 minutes when a well-timed run by Luis Suarez saw him finish at the near post following an exquisite ball from Phillipe Coutinho.
Valencia, however, found a foothold and arguably were the better side by the end of the half. The Portuguese winger threatened with three strikes before striker Rodrigo Moreno forced Marc-Andre ter Stegen to parry his shot off the bar after Valencia's pressure caused an errant pass by Barcelona's goalkeeper.
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Barcelona started the second half like they began the first though and five minutes after the restart, they doubled their advantage.