Florida State came from 15 points behind in the second half, limiting the Hokies to five points over the game's final 8:22.
The Seminoles won for the ninth time in 10 games and moved into a tie for the lead in the Atlantic Coast Conference.
After Ian Miller brought Florida State within two with 44 seconds remaining by hitting a 3-pointer, the Hokies suffered a missed 3-point attempt by Dorian Finney-Smith and two missed foul shots by Robert Brown. Brown's misses came with 11 seconds to go, setting up the Seminoles for a chance at the win.
Florida State's Jeff Peterson was cut off in his drive to the basket and he fired a pass to Snaer, who was wide open for his clutch 3-pointer.
Virginia Tech's Erick Green then missed a 3-point attempt under heavy pressure as time expired.
Miller scored 11 points for the Seminoles (18-7, 9-2 ACC) and was the only Florida State player in double figures. Green had 18 points to lead Virginia Tech (14-12, 3-8).
The Hokies have not won in Tallahassee in 22 years.
Snaer's basket was a rare bright spot in an otherwise poor shooting night for both teams. Virginia Tech made just 32 percent of its field goal attempts. Florida State hit 40 percent, but managed only one free throw in eight tries.