Ashley Barnes blasted into the top corner after City defender John Stones sliced his attempted clearance. However, Burnley hadn't won at City since 1973 and Argentina striker Aguero ensured that run continued. City, who last tasted defeat in domestic competition in their FA Cup semi-final against Arsenal in April, were level in the 56th minute when Aguero fired home from Ilkay Gundogan's pass.
Aguero then finished off a superb backheeled pass from Gundogan in the 58th minute. Sane prodded home to put the result beyond doubt in the 71st minute and Bernardo Silva made it four in the 82nd minute.