The England forward grabbed the opening goal in what proved a comfortable afternoon’s work for the champions at the Etihad Stadium.
It was the 26-year-old’s first strike in the Premier League since August in what has been a frustrating start to the season at club level.
Sterling has been unable to command a regular starting spot and, with his contract to expire at the end of next season, there has been speculation about his future.
City boss Guardiola said: “He needed that and in the first half he was an important player.
“He scored a brilliant goal, from an exceptional pass from Joao (Cancelo) again. He made a good game in a difficult one, because they defended really well.”
Guardiola also had words of praise for 19-year-old Cole Palmer, who shone on his first Premier League start, playing most of the game in the false nine position.
Guardiola said: “The striker position is the most difficult but as the game went on he felt more comfortable.
“He made a good assist, it was a good performance. He (now) already has 90 minutes in the Premier League in his mind. It is an incredible investment for the future.”
City were dominant throughout, with further goals coming from Rodri and Bernardo Silva.
Guardiola said: “It was really good, we’re very pleased. The last times we play against Rafa Benitez at Newcastle, always we struggled. We were better today, we conceded few chances and were patient.”
Everton offered little in terms of attack but manager Benitez took positives from the way his side maintained their organisation throughout.
Benitez said: “Obviously you have to be disappointed at the end but, in terms of the performance, we were well organised and defended with intensity.
“We weren’t a threat on the counter that we expected. We had two or three situations where we didn’t do enough.
“The first goal changed everything. We had chances on the counter but we didn’t create well. It was not easy. You can pay for any mistake.”
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies