Their 2-1 victory - achieved courtesy of goals from Luis Suárez and France defender Samuel Umtiti - means La Blaugrana have now gone 39 matches in La Liga without tasting defeat, more than any other side in Spanish league history.
The Spanish champions-elect will also be consoled by the thought that their bitter rivals Real Madrid are now languishing in fourth place in La Liga.
Barca showed few signs of lost confidence early on and after 15 minutes they took the lead, Coutinho drifting in from the right and, after spotting Suarez's angled run, poking a superb pass in behind.
Ter Stegen gifted the visitors another chance with a poor clearance but made amends in style, turning Rodrigo's effort onto the crossbar with an excellent one-handed save.
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.
Barca's goalkeeper has been excellent this season and he was kept busy as Valencia attacked, saving again from Rodrigo two minutes before half time.
Valencia played well, but for all their youthful verve they do not have the same talent or experience as a Barca side who beat them home and away in the Copa del Rey semi-finals.
Both Lionel Messi and Andres Iniesta went close to adding a third, and they were made to sweat after Valencia had halved the deficit in the closing minutes.
'This was already a very important game and after the defeat to Roma even more so. We knew that the fans were angry and we were also hurting.
Does that win secure the title? "We wanted to reach the final". We're focused. Obviously what happened in the Champions League was bad. "It seems like there's no merit to winning the league, now", he told beIN SPORTS.