Both teams scored twice in the first inning and it remained a 2-2 contest until the Yankees broke things open with their big seventh inning.
With Bruce Chen (0-4) pitching for the Royals, Robinson Cano led off the seventh with a single. The next two batters were retired, but Eduardo Nunez tripled home Cano and Nunez scored on a single by Chris Stewart.
That brought up Jeter, who hit a 2-2 pitch over the wall in center for his fifth home run of the season.
CC Sabathia (4-0) worked eight innings to get the win, giving up two runs on seven hits. He helped New York end a three-game losing streak.
After winning at home for the first time all season on Thursday, the Royals suffered their 11th home loss Friday.