Swann, who went 6-for-11 from 3-point range, had a game-high 28 points. The Seminoles had an 11-point lead with 6:54 remaining, but Blazers forward Lawrence Kinnard and guard Robert Vaden helped trim the lead to four. They had 19 and 17 points respectively.
Florida State (3-0) shot 71 percent from beyond the arc and a 73 percentage inside the paint in the second half.
Besides Swann, three other Seminoles scored in doubles digits, Toney Douglas had 11 and guard Jason Rich and forward Uche Echefu each had 10.
The Blazers (2-1) led 35-33 at halftime, but made just two free throws in the second half. They gave up 17 points off 13 turnovers in the game.
Guard Paul Delaney III added 12 points and five assists.