Dani Parejo gave Valencia brief hope with an 87th-minute penalty.
After an exhilarating week of Champions League football which saw Barcelona crash out of the competition and Real Madrid edge Juventus by the skin of their teeth, a lot has been made of the performances of the Spanish clubs' two star men. "It was more important that we picked ourselves up after a hard week", Valverde told a news conference.
Valencia stay third, one point ahead of Real Madrid, who are also in action on Sunday, away to Malaga.
"The week has been hard and that hard week affects everyone, including the fans".
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.
He could still win a league and cup double this year with Barcelona.
What are your thoughts on setting a new unbeaten Liga record?
"Records are there to be broken", Suarez told beIN Sports.
We tried to continue the great league showing after what happened the other day.
Despite their exertions in Rome, Valverde resisted the temptation to rest key players, with Philippe Coutinho and Paulinho coming in for Ivan Rakitic and Nelson Semedo.
Luis Suarez opened the scoring for Barcelona vs Valencia. Suarez took the finish first time and swept the ball inside the near post. 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 outswinging corner from which Samuel Umtiti headed in Barca's second in the 51st minute, shortly after Gerard Pique had saved Umtiti's blushes by clearing a shot from Valencia forward Santi Mina off the line following a slip by the France defender.
Ter Stegen, who is usually so assured with the ball at his feet, was under no immediate pressure before playing a poor pass out which eventually fell to Rodrigo, who failed to capitalize on the massive chance as the German goalkeeper redeemed himself with a fine save tipped onto the woodwork.
A couple of acrobatic attempts from Andres Iniesta and Lionel Messi came very close to putting the game out of sight, but a nervy last five minutes was in order after substitute Ousmane Dembele flew in on Jose Gaya in the box, a penalty was awarded.
Mikel Oyarzabal scored his third goal in two matches to give Real Sociedad a 1-0 win at relegation-threatened Las Palmas, while Miguel Guerrero gave Leganes a 1-0 win over Celta Vigo.