A huge Catalan flag and banners reading "justice" in Catalan and English were displayed before kick-off after eight ministers of the Catalan government deposed by Madrid were detained pending a possible trial for their roles in the drive for Catalan independence.
Loud cries of "freedom" also rang around Europe's largest stadium sporadically throughout the 90 minutes.
Two other banners reading "Freedom for political prisoners" and "Europe shame on you" were held up by the Barca singing section behind one of the goals.
"The team are showing that is isn't a distraction," said Valverde.
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"People come to the Camp Nou to express themselves peacefully and support their team. We play for them."
The hosts could have scored three times in the opening 10 minutes as Clement Lenglet cleared off the line from Sergio Busquets, David Soria denied Luis Suarez and Ivan Rakitic fired a long-range effort inches wide.
"You have to take the chance given to you by the coach," Alcacer told BeIN Sports Spain.
"More than my game you have to look at it from a team perspective and these games where you are made to suffer mean more."
Suarez's cross-field pass was mis-controlled horribly by Sergio Escudero and fell perfectly for Alcacer to slot past the advancing Soria.
Barely a threat before half-time, Sevilla came out a different side after the break and levelled just before the hour mark when Guido Pizarro bulleted home Ever Banega's corner.
On his 600th Barca appearance, Lionel Messi had the chance to make the game safe when his low effort was saved by Soria, but Barca held on to move 11 points clear of Real Madrid, who face Las Palmas on Sunday (1945 GMT).
"We are top, we aren't dropping points and we are going into the international break happy," added Valverde.
"Afterwards we have a tough schedule, we have strong rivals behind us and we need to remain srong to stay on top."
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Barca travel to Valencia on November 26 and Los Che remain their closest challengers, four points back, as they swept aside Leganes 3-0 for a club record seventh straight league win.
"No one will go undefeated through 38 games, but we are going to enjoy the moment," said Valencia coach Marcelino Garcia Toral.
"In the dressing room there is no euphoria, there is realism and constant analysis.
"We know how difficult it will be to keep this up, it's practically impossible."
Dani Parejo's clever free-kick that skidded underneath the Leganes wall got Valencia off to a perfect start on 14 minutes.
And the team spirit in this Valencia side was demonstrated when habitual penalty-taker Parejo let Santi Mina take responsibility from the spot eight minutes from time to round off the scoring.
- Partey bail out -
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By contrast, Atletico Madrid's struggle for goals continues but Diego Simeone's men were bailed out by Thomas Partey's 91st-minute winner in a 1-0 victory at Deportivo la Coruna.
Atletico suffered from a familiar lack of creativity at Riazor with Simeone even substituting star frontman Antoine Griezmann 10 minutes from time.
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