Ernesto Valverde's side lead nearest challengers Atletico Madrid by 14 points in the standings, with Atletico hosting Levante and fourth-placed Real visiting basement club Malaga on Sunday.
They started positively on Saturday but it was Valverde's side who took the lead in the 15th minute.
Heavy rain and Wednesday's defeat in Italy limited the attendance to 69,544, 16,000 less than Camp Nou's last daytime home game a month ago, but despite the flat atmosphere, the fans' efforts to attend were rewarded by an entertaining game.
Barcelona were in the doldrums when the season began after they were thrashed by Real Madrid in the Spanish Super Cup. As well as setting a new La Liga unbeaten record, Barca need to avoid defeat in just six more league matches to go an entire league season unbeaten. Soler played in Rodrigo Moreno but Ter Stegen made up for his mistake by pushing the shot onto the bar.
Club-record signing Coutinho then delivered an out-swinging corner from which Samuel Umtiti headed in Barca's second in the 51st minute. A late goal from Daniel Parejo could not save Valencia as they went down fighting at the Camp Nou. "Today we played against the third-placed team, and we won". "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".
"We have not lost much but the game the other day was important and you have the feeling that we have disappointed people". We have important things to achieve and we won't lose face.
Barca have reached the Copa del Rey final, where they face Sevilla next Saturday in Madrid, a game which could see the Catalans come closer to a domestic double. "It seems like there's no merit to winning the league, now", he told beIN SPORTS.