Weatherford, who passed for 336 yards, also connected on a 17-yard scoring pass with Greg Carr that gave the Seminoles a 7-3 lead early in the second half.
After managing just 1 yard rushing against Miami in their season-opening victory, the Seminoles again were stalled on the ground. Florida State gained 45 yards on 28 carries, nearly all coming in the fourth quarter.
Freshman Antone Smith led Florida State with 25 yards rushing on a half dozen carries and Lorenzo Booker added 18, also on six tries.
Davis' muff with 12:54 left was recovered by Elbert Mack at Florida State's 31 and Haugabook scored on a 1-yard run to give Troy a 17-10 lead.
Gary Cismesia, who had earlier missed from 39 yards, tied the game at 10-10 with a 44-yard field goal with 4:04 left in the third quarter.
The Seminoles scored on their first drive of the second half on Carr's leaping catch in the end zone.
But Troy answered with an 80-yard scoring drive culminated by Haugabook's 3-yard touchdown strike to Toris Rutledge.
Troy had its chances to put more points on the board.
Despite moving inside Florida State's 20 on three occasions in the first half, the Trojans managed just one field goal - a 39-yard kick by Whibbs with 4:41 left in the second quarter that stood for a 3-0 halftime lead.
Troy made it to Florida State's 3 on the game's opening drive, but Roger Williams intercepted Haugabook's pass in the end zone after it was first tipped by cornerback Tony Carter.
The Trojans had a second scoring opportunity moments later in the first quarter, but Whibbs 31-yard field goal try was blocked by Florida State's Everette Brown.
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