City moved 16 points clear of nearest challengers and local rivals Manchester United, and now need just six wins and two draws from their remaining 11 games to clinch the title.
Aguero was the star of the show, taking his goal tally for the season to 27 with his 12th City hat-trick and his career total for the Blues to 196 in seven seasons.
City took the lead after just three minutes, Raheem Sterling meeting a curling cross from Kevin De Bruyne at the far post for his 20th goal of the season.
But a howler from City defender Nicolas Otamendi allowed Leicester to level in the 24th minute through England striker Jamie Vardy.
Otamendi played the ball into the path of Vardy, who evaded two challenges before finding the net, via a deflection off City's £57million defender Aymeric Laporte.
It was a deserved leveller for the Foxes, who were well organised and kept City on their toes with their swift counter-attacking, but the visitors were unable to remain on level terms.
De Bruyne was once again the provider, three minutes after the restart, producing another teasing ball into the six-yard box for Aguero to score with the simplest of finishes.
Aguero claimed his second in the 53rd minute, before clinching his hat-trick with an exquisite chipped finish in the 77th minute after Kasper Schmeichel had played the ball straight to him.
Riyad Mahrez, denied a deadline day move to City after Leicester rejected a £60m bid for him, came back in from the cold after going AWOL, coming on in the second-half, but he was unable to inspire a comeback for the Foxes.
Aguero scored his fourth with an explosive shot from outside of the area in the 90th minute to make it 5-1 for Pep Guardiola's rampant side.
MAN CITY 5 - 1 LEICESTER
HT 1-1
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