Bruno Zuculini gave Manuel Pellegrini's men an early lead before C.J Sapong equalised for the hosts, though the scores were not level for long, Dedryck Boyata restoring City's lead on the stroke of half-time.
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The tone of the contest was set early as Zuculini finished with power and precision into the bottom left corner of Sporting KC's goal.
Peter Vermes' men almost replied immediately, with Sapong's volley from a Soony Saad cross coming back off the crossbar while Dom Dwyer had a goal ruled out due to an offside flag from a free-kick in the 10th minute.
City's attacking game rarely let up, however, with Nigerian teenager Iheanacho forcing Sporting goalkeeper Andy Gruenebaum to tip two long-range shots away in two minutes.
Sporting found a deserved equaliser though, as Benny Feilhaber's cross into the area found Sapong, who had time to take a touch and finish past the stranded Willy Caballero on the half-hour mark.
Stevan Jovetic had a one-on-one chance with Gruenebaum late in the half, only for a superb last-gasp challenge from Collin to deny the Montenegrin forward.
However, he then lost Boyata at a set-piece as City took a lead into the interval.
Both coaches made a number of changes at half-time, Sporting KC bringing in a fresh XI while City introduced Micah Richards for Gael Clichy.
Sal Zizzo was at the heart of multiple Sporting KC chances for an equaliser, sending a diving header wide and also finding Michael Kafari in a dangerous area - but his team-mate was unable to finish under pressure.
And they were made to pay, City going on to seal the victory as Kolarov scored from 12 yards after Scott Sinclair was fouled in the area by Kafari, before Iheanacho capped an impressive display with a goal.