Villa scored a fine second halfway through the first period and also bagged the fifth of the night right at the end to bring his recent goal drought to an end.
"We never doubted him," Guardiola said.
"He has played for Sporting (Gijon), for Zaragoza, for Valencia, and scored goals for all of them, so we knew his signing was a guarantee."
The Barca coach was also pleased with Alves, who pounced on a poor headed back-pass from Ndri Romaric to score an opportunistic third for the Catalans.
"He scored a great goal. He has great intensity and great stamina. He has shown that since he has been here and he is a very important player for us," he said.