Luis Suarez and Samuel Umtiti were both on target as Barca passed the 38 matches Real Sociedad managed without defeat between 1979 and 1980. Dani Parejo gave Valencia brief hope with an 87th-minute penalty.
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 are now 14 points clear at the top of the table, before second-placed Atletico Madrid play their game in hand against Levante on Sunday.
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