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.
Valencia stay third, one point ahead of Real Madrid, who are also in action on Sunday, away to Malaga.
"The value of these three points is great, they are three points of gold," Valverde said.
"The week has been hard and that hard week affects everyone, including the fans.
"We have not lost much but the game the other day was important and you have the feeling that we have disappointed people. You want to repay them."
There is no doubt Barca's shock defeat in Italy still lingers, and may still, even if the Catalans secure the first part of an expected domestic double by winning the Copa del Rey next weekend.
But it should take little away from their faultless form in the league, which means the last time they tasted defeat outside a cup competition was against Malaga just over 12 months ago.
This was already a club record run, now eight games better than the 31 unbeaten Pep Guardiola's brilliant team strung together in the season of 2010-11.
It would now seem only the home Clasico against Real Madrid on May 6, and perhaps an awkward trip to Celta Vigo on Tuesday, stand in the way of Barcelona finishing the league campaign as invincibles.
"Records are there to be broken," Suarez told beIN Sports. "The public can be angry about the Champions League, like us, but this is a recognition of the great season we are having in the league, which now seems to have been forgotten."