Chris Singleton added 18 points for Florida State (12-5, 2-1 Atlantic Coast Conference), which made five free throws in the final 33 seconds to hold off the defending national champions. It was the third time since 2002 that the Seminoles beat a top-ranked Duke team at home.
The Blue Devils hadn't lost since a 79-72 setback on March 3, 2010, at Maryland. From there, they went on to win the ACC and NCAA tournaments for their fourth national title.
The 25-game winning streak was the second-longest in Duke history.
The Seminoles led 28-24 at halftime and by as many as 11 early in the second half, but the game was tight to the finish.
Kitchen, a 6-foot-4 senior guard, scored 17 points in the second half and led the Seminoles with a team-high 10 rebounds for his second double-double of the season.
Singleton's two free throws with 33 seconds left gave the Seminoles a 63-58 lead, but Smith's 3-pointer chopped the Duke deficit to two with 26.9 seconds remaining.
Duke came into the game averaging nearly 88 points, having outscored its opponents by just under 25 points per game this season.
Florida State had lost three of four, including its past two games against Auburn and Virginia Tech.
Smith's 3 with 2:26 left pulled Duke to 59-58, but Kitchen countered with a baseline pull-up to give Florida State a 61-58 edge with 2:01 to go.
Singler missed a 3-pointer with a minute remaining that would've tied the score.
Singler didn't get his first field goal until the opening minute of the second half on a goaltending call on Singleton, but then heated up quickly, hitting five of his next six shots from 3-point distance to help wipe out Florida State's 40-29 cushion early in the second half.
Duke caught up with a 13-2 run and tied it at 42 on Andre Dawkins' three free throws after being fouled by Singleton on a 3-pointer. Kitchen answered again, this time with a 3-pointer from the top of the circle, and Duke could never get the lead.
Bernard James put back a pair of offensive rebounds in the final 1:15 of the first half to give Florida State a 28-24 lead at the break.
Duke came into the game shooting just under 50 percent for the season, but went only 9 of 32 for a 28.1 percent effort in the first half against Florida State's rangy defense.
Florida State's 11-6 lead on Singleton's jumper was the largest either team had in a first half that featured eight lead changes and seven ties.
Duke's biggest lead was three points, 16-13 and 24-21.