Manchester City roared back from a two-goal half-time deficit to score three times after the break.
Manchester City demolished Chelsea 6-0 to go top while Tottenham Hotspur cemented their third place with a 3-1 win over Leicester City.
Manchester City's quest for four trophies continued with a 5-0 thrashing of Burnley in FA Cup.
Manchester City recently suffered back-to-back defeats against Crystal Palace and Leicester City.
The win over Everton, moved Manchester City two points ahead of Liverpool, who host Manchester United on Sunday.
Manchester City are now 12 points clear of Manchester United and moved two points ahead of Liverpool at the top.
Jose Mourinho said of Sergio Aguero that "there are little things in his game I am not a fan of".
The former England defender feels Chelsea, Liverpool and Arsenal will finish in the top four.
Manchester City remain top of the table on goal difference, but both teams are now locked with Chelsea.
Pep Guardiola believes the Egypt star must score prolifically over a period of multiple years to match Sergio Aguero's achievements.
The 30-year-old Argentina international put pen to paper on a deal that will see him through to the end of the 2021 season.
Aguero, who turned 30 in the close-season, has now scored 14 times in his last eight Premier League games at City's Etihad Stadium.
The last side to win the Community Shield and then go on to clinch the Premier League title were Manchester United in 2010-11.
France beat Lionel Messi's Argentina 4-3 in a thrilling last 16 World Cup match on Saturday as teenager Kylian Mbappe scored two goals in a superb performance in Kazan.
Argentina have to get past Nigeria in their last league match to qualify for the knockouts.
Argentina, with only one point from two matches, are teetering on the edge of inglorious elimination.
Lionel Messi is yet to win a major international tournament and time is running out with his 31st birthday looming.
Aguero scored 21 goals for City in the Premier League this season despite it being cut short after he aggravated an injury to his right knee.