The 'Citizens' were looking to capitalise after Chelsea had dropped points earlier into the day at home to Manchester United, and Aguero got them off to the perfect start with a quarter of an hour gone.
He finished off a well worked move down the left following some good work from David Silva, who remains a key player for City in the absence of Kevin de Bruyne.
The Spaniard put in a low cross which evaded several Burnley defenders and found Aguero at the back post.
The Argentine never misses from range like this, and he was soon off celebrating after tucking a finish into the bottom corner. City will go top of the league with a win.