First-half goals from Leroy Sane, Gabriel Jesus and Raheem Sterling wrapped up the victory, ensuring Yannick Bolasie's strike after the break was merely a consolation.
City – beaten 4-0 in this fixture last season – can now claim the title by beating bitter rivals Manchester United next weekend, with a Champions League quarter-final first leg against Liverpool to negotiate before that.
A delighted Guardiola, who sealed his 50th Premier League victory , told BT Sport : "We knew we must win all games. We did our job in the first half – it was so, so good.
"We controlled the game and it was a huge victory. It was the first time as a manager I was able to beat Everton.
"It was a long time we weren't together [during the international break] so you always think 'what could happen', but it was good.
"We were clinical especially in the first half. Everybody committed to win the game. Now it is one more game and we will be champions.
"[For] the fans it is significant. It is special. It is important we win – no matter where. Of course the most important thing is these two games."
With the Carabao Cup in the trophy cabinet and the top-flight crown imminent, conquering Europe is the key to City's treble dreams and Guardiola knows his side face a tough challenge against Liverpool, the only team to beat them in the league this season.
"We have to go to Anfield with good feelings," he added. "Now we have a few days to prepare for this game."