Todd Galloway's first points of the game, two free throws with 45 seconds remaining, gave the Seminoles the lead at 71-70.
Adam Waleskowski and Pickett each added two free throws in the final 18 seconds to seal the win.
Pickett's 3-pointer with 1:17 left pulled Florida State within 70-69.
Nate Johnson and Waleskowski kept Florida State in the game during the first half, combining for 26 of the team's 36 points as Pickett went scoreless. Johnson hit all four of his 3-point attempts while Waleskowski contributed 12 points and five rebounds.
Johnson led all scorers with 19 points while Waleskowski finished with a career-high 16 points and eight rebounds.
The lead changed hands seven times in the first half and there were 10 ties.