Twin vehicle attacks on Thursday killed 14 people and wounded around 120 in Barcelona's bustling Las Ramblas boulevard and the nearby seaside resort of Cambrils.
A minute's silence was held before kick-off, whilst Barcelona players wore black armbands and shirts with 'Barcelona' replacing individual names on the back.
"What happened was terrible, we hope this stops now because we are not afraid," Barca winger Gerard Deulofeu, who set up both goals, told BeIN Sports Spain. "This victory is for those affected."
A defiant attitude was on show in the stands, although in common with many matches against weaker opposition, the 99,000 capacity Camp Nou was far from full.
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After the attack some fans, especially tourists, returned their tickets, the club said without giving figures.
"Their money was refunded to everyone, the circumstances are special and understandable," a club spokesman said.
- 'Not afraid' -
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Fans in the Barca singing section borrowed a line from the club's anthem in a banner that read: "No one can ever break us," whilst chants of "we are not afraid" rang out after the minute's silence.
"I thought there would be like a collective hysteria but I see everything is normal," added Sandra Lorenzo, 41, as she sold drinks next to the stadium.
"I have worked here for 25 years at every match. They are not going to make me stay at home."
Prior to the attacks, Barca had endured a difficult start to the season on the field as shorn of Neymar following his world record 222 million euro ($261 million) move to Paris Saint-Germain, the Catalans were swept aside 5-1 on aggregate by Real Madrid in the Spanish Super Cup.
However, despite also missing the injured Luis Suarez and Andres Iniesta, Barca rose to the challenge of raising the city's spirits with a dominant display.
"In the end you always have to move forward," said Valverde.
"Our idea was to be able to dedicate this victory to those affected."
With the mayor of Cambrils Cami Mendoza and chiefs of Catalonia's regional police force among those watching on, captain Lionel Messi led by example with Deolofeu and Paco Alcacer struggling to fill Suarez and Neymar's shoes up front.
Deulofeu was the provider once more when Barca doubled their advantage three minutes later as Sergi Roberto slotted home from close range.
Messi also posed the biggest threat of a low key second- half as he struck the woodwork twice more with rasping shots from outside the area.