They became only the third team to win in the league at Goodison Park this year and the first since late March.
"It was a great win for us," said Benitez.
"The team showed their character and quality and although we made mistakes at the beginning the reaction was really good.
"We knew they could be tough but we had confidence in the players.
"We put Ramires on the right side against Leighton Baines and he gave us a great game too."