Barcelona moved 14 points ahead of second-placed Atletico Madrid, before Atleti's match against Levante on Sunday, while Valencia sit a further three points back following the end of their five-match winning run.
A terrible back-pass from Barca nearly went pear-shaped as it freed in Rodrigo, who took a touch before forcing Ter Stegen pushing his shot to the crossbar for a corner.
The two goals aside, the league leaders were kept relatively quiet as an attacking force.
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.
"We issued a plea for information to those fans who may have been involved in these incidents", read a club statement on their official website.
"We played a good match today, too bad we were missing our finishing touch", Valencia coach Marcelino Garcia Toral said. We're sorry for what happened.
Suarez, who opened the scoring before Samuel Umtiti's header sealed the win, says the reaction from some of the press and the fans makes it feel as though winning the domestic title nearly does not matter. "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 wanted to reach the final".
Even that would feel like a slight let down after European elimination, but this has been a successful year with the prospect now, with six league games to go of the campaign, of a first ever unbeaten season.
Valverde admitted that Messi was devastated by the loss although he urged the five-time Ballon d'Or victor to put the disappointment behind him and do his utmost to ensure that they win La Liga and Copa del Rey titles.