The Argentina star struck twice in the first half at Etihad Stadium and added a third with a penalty to put City 5-0 up soon after the interval and earn a share of top spot alongside former Southampton, Blackburn Rovers and Newcastle United striker Shearer.
City went on to win the match 6-0, with Aguero taken off after 65 minutes to a huge ovation from the Etihad faithful.
Shearer, who is the Premier League’s all-time top scorer, notched the last of his 11 Premier League hat-tricks 20 years ago for the Magpies in September 1999.
Aguero, City's all-time top scorer with 220 goals in all competitions, also became the sixth player to register 200 goal involvements for a single Premier League side in the process while surpassing Tommy Johnson and Eric Brook as the club's most prolific player in league fixtures.
The 30-year-old's dominant display against a thoroughly outplayed Chelsea marked his second treble in the space of a week, having inflicted similar damage upon Arsenal in City’s 3-1 victory seven days earlier.
With nine Premier League hat-tricks at the Etihad, Aguero has also set a record for the most trebles by a player at a single ground, breaking the record held by Thierry Henry at Highbury.
Former Liverpool, Leeds and Manchester City striker Robbie Fowler is third on the hat-trick leaderboard with nine, while Tottenham's Harry Kane (eight) is the only other active Premier League player to have notched more than three.
Michael Owen and Thierry Henry finished their careers with eight apiece, one more than Wayne Rooney's seven and two ahead of the six Luis Suarez managed for Liverpool.
Two goals from Raheem Sterling and another from Ilkay Gundogan completed a comprehensive victory for Pep Guardiola’s men at Etihad Stadium.
It meant City returned to the top of the Premier League on goal difference ahead of Liverpool, albeit having played a game more.
City’s next three matches come in three different competitions, with League Two Newport County next up in the FA Cup fifth round on Saturday.