Jason Geathers scored on an 11-yard run with 5:17 left to give the Hurricanes a one-point lead. Willis McGahee, who carried 26 times for 96 yards, had dashed 68 yards on a screen pass from Ken Dorsey on the previous play.
The Seminoles then moved into position for a game-winning field goal. But Beitia, who had connected earlier in the game from 45 and 42 yards, hooked his kick to the left after a poor snap, adding another amazing chapter to one of college football's best rivalries.
Florida State lost close games to Miami in 1991 and 1992 as field goal attempts sailed wide right in the final seconds. Two years ago, a 49-yard attempt by Matt Munyon also was wide right, giving the Hurricanes a three-point win.
"I can't believe we lost the game like this again. I thought we had it," Florida State coach Bobby Bowden said. "I went out to shake (Beitia's) hand. I thought he hit it. I've had that picture so many times before in my career. I can't stand it.
"Our kids did not deserve to lose this game."
Despite a sluggish performance in which it was penalized 14 times for 109 yards, Miami (6-0) extended the nation's longest winning streak to 28 games and won for the 20th straight time at the Orange Bowl.
Miami overcame a huge game from Florida State's Greg Jones, who carried 31 times for 189 yards and a score.
But it was not enough as Florida State (5-2), which hoped to return to list of the sport's elite with a win on Saturday, lost to the Hurricanes for the third straight time.
"What was going through my head? I was not nervous," Beitia said. "I was thinking, `Just make the kick, just make the kick,' the same thing that always goes through my head. Was it a bad snap or a bad hold? I don't know the answer. It's a blur."
Dorsey was the victim of several dropped passes but still threw for 362 yards, completing 20 of 42 passes with two interceptions. He took control when the Hurricanes needed him most, throwing a two-yard touchdown pass to Kevin Beard with 8:10 left to cut the deficit to 27-21.
"I think we realized the game was in jeopardy and we took it upon ourselves to make something happen," Dorsey said. "Thankfully, the defense came up big."
Florida State rolled up 296 yards on the ground behind Jones, who scored on a 12-yard run to increase the Seminoles' lead to 27-14 with 11:44 left.
The Hurricanes have won their first 18 games under Larry Coker, who is off to the best start by any coach in the last half century. Miami, which topped Florida last month, passed yet another stiff test. Its next major challenge likely will come Nov. 9 at Tennessee.
"This was a great team victory and we'll remember it for a long time," Coker said. "We never gave up. We made a lot of mistakes. Florida State, as we know, is an excellent football team. They came to play, as we knew they would."
"I know we made a lot more mistakes than Florida State did, but I know a lot of us gave an effort," Miami center Brett Romberg added. "I kind of think we earned it. Some of us think we earned it."
The Hurricanes looked impressive on their opening drive, marching 91 yards in 13 plays and taking nearly eight minutes off the clock before McGahee broke several tackles and scored on a four-yard run.
The teams committed turnovers on consecutive plays in the second quarter when Leon Washington fumbled a punt and Dorsey immediately fumbled. The Seminoles moved downfield and Nick Maddox scored on a 30-yard run to tie it at 7-7.
Beitia kicked a 45-yard field goal to give the Seminoles their first lead.
Florida State continued to move the ball on the ground as runs of 14 yards by Jones and 17 yards by Maddox set up a 10-yard touchdown pass over the middle from Chris Rix to Talman Gardner.
"I'm speechless. I've never been so tired in all my life," said Rix, who completed just eight of 19 passes for 83 yards. "One play and we had this game. We lost by inches. It's a tough way to lose."
Miami cut it to 17-14 at halftime on a five-yard toss from Dorsey to Kellen Winslow with 26 seconds left in the second quarter.
But even with the touchdown, Miami trailed at the half for the first time under Coker.