The Blaugrana boss recently suffered the relapse of the disease, which kept him from taking his place on the bench for part of last season, and subsequently underwent surgery to remove the tumour.
"We are here to help him be," the Brazilian told O Estado de Sao Paulo. "That's why every victory is dedicated to him. Football comes second now, because he is struggling for his life."
Vilanova had led Barca to its best-ever start to a Liga season, and although the club holds a 16-point lead over reigning champion Real Madrid, Alves is adamant that the title isn't decided.
"The gap is more than considerable," he explained. "But we should remain grounded as we still have many games left and the championship is far from over. I'm not surprised by our results so far.
He added, "We are reaping the fruits of our labour. We worked hard, and the results are following."
The former Sevilla man has been linked with a move away from Camp Nou in recent weeks, but is adamant that he has no intention of leaving.
"Those are interventions made to destabilize us. I feel good and I want to stay," Alves said.
Barcelona gets back to action after the winter hiatus by entertaining Espanyol on January 5.