Smith went 24-of-41 through the air for 288 yards, overcoming a pair of interceptions as the Chiefs improved to 4-0 for the first time since 2003.
Jamaal Charles racked up 127 yards of total offense from scrimmage and caught one of Smith's TD tosses while Kansas City's defense also made a big contribution, limiting the Giants to 298 total yards.
Dexter McCluster ran back a punt 89 yards for a score in the victory.
Eli Manning was held to 18-of-37 passing for 217 yards with one touchdown and an interception for the Giants, who fell to 0-4 for the first time since 1987.
Megyn Kelly: Santa Claus and Jesus are both white men
Susan Sarandon: I was stoned at almost every awards show