Neither team could break the scoreless deadlock until the 6th minute of stoppage time, when Smith broke free on the left wing and the rookie put a pass from Marco Di Vaio behind Kansas City goalkeeper Jimmy Nielsen for the game-winner.
The late tally enabled the Impact (10-5-5) to snap a five-game winless streak.
Nielsen finished with three saves for SKC (10-6-6), which retained first place in the Eastern Conference with 36 points despite loss, one ahead of Montreal and New York.
Exploding whale video goes viral on Internet
Couple mistakenly served bag of cash at McDonald's drive-thru