The Blaugrana secured three points in the Catalan derby through a 77th-minute Lionel Messi penalty to maintain pressure on first-place Atletico Madrid, which remains just a point ahead.
Barcelona remains in contention for its 23rd league title but Alves reminded fans and pundits alike that comfortable wins are rare pleasures in a title run.
"We are ready to fight until the end," the 30-year-old told reporters after the game. "We never lost our intensity, our rivals play football too – they are playing for their lives in this competition, it makes it all very difficult. Barca may not win all their games comfortably, sometimes we can, other times we cannot."
Gerardo Martino's side was regularly frustrated by Los Periquitos but Alves said Barca had expected a tough test against its cross-city rivals.
"It was hard to win here because of who we played against," he said. "They apply a lot of pressure and they are intense in their approach to the game. We knew that it would be difficult, but I thought we played a great first half. We gave it our all. We're doing well and we're confident, but we know how hard it's going to be."
The victory leaves Barcelona on 75 points from 31 matches, a point behind Atletico with the duo facing off at Camp Nou on the final day of the season.