WVU converted a fourth-and-1 on the drive and later a third-and-17 thanks to a personal foul penalty against the Bulls.
"We've been through that so many times," Smith said. "The two-minute drill is basically our offense. We've dealt with high-pressure situations numerous times before."
WVU, which allowed game-changing kickoff return touchdowns in losses to LSU and Syracuse, then watched USF return the kickoff 52 yards. A third-down conversion on a Daniels run gave the Bulls a first down inside the WVU 30, but Daniels gambled and Goode made him pay.
"I sat back and watched him," Goode said. "He's a quick guy, but I got to him and I tried to strike him and swing at the ball. I didn't know it was out."
Rigg, who missed two games after fracturing his left hand against LSU, was first to the ball before players from both teams piled on top of Rigg and his padded left hand.
"I knew we were OK when I saw Doug get up and put his one club hand and his one good hand in the air," Goode said.
The Mountaineers took over with 3:02 remaining and no timeouts left to call. The drive moved until it was fourth-and-10 at the USF 42. Smith scanned the right side and then came back left to Bailey, who extended to make the catch.
"The previous couple plays, when I stood in the pocket for 10, 12 seconds, they were triple-teaming him," Smith said. "But that's something we've been doing since high school. It's like sandlot football."
The drive covered 58 yards in 11 plays to set up Bitancurt's third field goal of the game and his second career game-winner. He beat Pitt with a 43-yard kick in 2009.
"It felt good coming off my foot," said Bitancurt, who hit the right upright from 38 yards away in the first quarter, but was good from 23 and 42 yards before his winner. "I only took one quick glance at it."
The Mountaineers finished with 365 yards of offense, with 135 coming in the final two drives.
"We hadn't done anything all game," Smith said. "We'd move the ball and sputter, move the ball and sputter. It was about time to make some plays."
Smith completed 24 of 35 passes for 242 yards, but didn't throw a touchdown pass for the first time in 15 games. Bailey caught seven passes for 80 yards and Garrison ran 16 times for 87 yards. WVU was just 2-for-14 on third down -- 0-for-7 in the second half -- but 3-for-3 on fourth down.
In addition to Austin's punt return, receiver Willie Milhouse blocked a punt to set up a field goal in the first quarter. Defensive end Will Clarke had a game-high 8.5 tackles.
The Bulls had 396 yards of offense and Daniels, a game-time decision after missing last week's game with a right shoulder injury, was 21-for-44 for 226 yards, one touchdown and one interception. He started 3-for-13 for 8 yards and an interception.
Darrell Scott ran for 92 yards on 14 carries. The Bulls were 10-for-19 on third down on offense and the defense, which was No. 2 in the country in sacks and tackles for a loss, had one sacks and six tackles for a loss.