TALLAHASSEE, Fla. -- Jimbo Fisher vs. the state of Florida?

Oh, he's good.

Real, real good.

The seventh-year Florida State head coach, whose rumored future is no longer in doubt after LSU filled its head coaching position earlier in the day Saturday, improved to 17-1 all-time against teams from the Sunshine State on Saturday night with a 31-13 win against No. 15 Florida.

Fisher, who is now 6-1 just against the Gators -- including four wins in a row vs. Florida -- said afterward the win felt even better after a long and trying week.

"It feels great (to get the win), but I ignore all the rumors. I ignore it and move on. I love Florida State, love what we're doing and I think we can do it for a long time," said Fisher, who has a long-term contract with Florida State through the 2022 season -- but he's been the subject of reports for two weeks linking him to the LSU position. "When you're successful, people (mention your name for other jobs). It's just part of it. I love the hell out of it (here), and I've been upfront and honest with everyone the whole time."

No. 14 Florida State's regular season ended with its fourth straight win, and the Seminoles will now await their bowl-game pairing. But the Gators' year isn't over; they'll play for the SEC Championship in Atlanta next week against No. 1 Alabama.

Seminoles running back Dalvin Cook made a late Heisman Trophy push with 26 carries for 153 yards and one score in the win, becoming the school's career touchdown leader one week after he broke the Seminoles' all-time rushing record. The junior, who is expected to jump to the NFL after this season, received a huge standing ovation from the home crowd late in the fourth quarter in what was likely his final game in Tallahassee.

"No. 4 ..." Fisher said of Cook before pausing for several seconds and then adding: "I mean, wow. I'm blessed to coach him. You see the player, you see the toughness, but don't forget about his selflessness, his leadership. I don't know what else to say about him. Just outstanding. What a dadgum football player and person."

When Cook was asked whether he'd played his final game at Doak Campbell Stadium, he simply smiled and said, "I can't answer that. We enjoyed our year, man. Now we just need to go finish it the right way."

The Seminoles led just 10-6 midway through the third quarter of a tight game when Florida State quarterback Deondre Francois gave his team some breathing room with a 46-yard touchdown pass to receiver Travis Rudolph. The Seminoles' very next drive also ended with a touchdown, this time a 27-yard run from fullback Freddie Stevenson with 12:51 left in the fourth quarter to put Florida State comfortably ahead 24-6.

"He led us and made some plays and kept his poise," Fisher said of Francois. "For a young player, in the magnitude of a game like that against Florida, to keep your poise is hard. You have no idea for a quarterback how hard that is to do."

Francois -- the top-rated rookie quarterback in FBS -- finished 15 of 26 for 138 yards, one touchdown passing and another score rushing, the latter touchdown coming with one minute left to play to seal the win. Rudolph led the Seminoles' receiving attack with four catches for 63 yards.

For the second straight year, the Gators -- who were 0-for-12 on third-down conversions Saturday -- failed to score an offensive touchdown in their meeting with the Seminoles. Florida lost last year's game 27-2 in Gainesville.

The lone Florida offensive points Saturday night came from two field goals by kicker Eddy Pinerio -- one in the first half, one in the second. The Gators' only touchdown Saturday was the result of a scoop-and-score by defensive back Marcell Harris on a fumbled Florida State punt return early in the fourth quarter.

"We couldn't block. We couldn't protect, but I'm proud of those guys in that locker room. This hurts," Florida head coach Jim McElwain, who is now 0-2 against Florida, said during a testy postgame press conference with the media that lasted less than five minutes and ended when a reporter asked McElwain if he thought the Gators could bounce back with the top-ranked Crimson Tide next week. "We'll get home about 3 in the morning probably. I don't know whether they'll come back or not. It's going to be a heck of a test. ... Yeah, I'm concerned. These guys have been through a ton now and they played their tails off today and it hurts, but you know, as a competitor you tear off the rearview mirror and you go forward. Our team will be ready. I have no idea what kind of question that was, but to question that locker room right there and those players."

The Florida State defense held Florida to 207 total yards of offense, and Gators quarterback Austin Appleby struggled to a season-low 149 yards passing.

"I know this Gator team. I know this Gator offense," Appleby said. "(This loss) stung. But we're gonna come back."

Florida State added to its FBS-leading sack total with six more Saturday night, including two from defensive lineman DeMarcus Walker, who now leads the nation with 15 on the season. Linebackers Matthew Thomas and Josh Sweat led the Seminoles' defense with seven tackles each.

Florida had a chance to deliver the first blow in the 61st edition of the Sunshine State rivalry Saturday night, driving all the way down to the Seminoles' 2-yard line on the opening possession before falling short on third down and facing a fourth and goal. But rather than take an easy try at a 19-yard field goal and the first points of the game, McElwain opted to go for it. Appleby's pass attempt, however, was incomplete, turning the ball over on downs to Florida State.

The Seminoles looked to be on their way to taking advantage of the early mistake, driving 61 yards on their opening march to Florida's 33-yard line. But when the drive stalled, Florida State tried a 50-yard field-goal attempt, which was missed badly by kicker Ricky Aguayo.

Florida took over, but two plays later, Appleby was strip-sacked by Sweat and Walker recovered. Two plays after that, Cook and the Seminoles hit pay dirt with a 17-yard rushing touchdown to go ahead 7-0 with 4:40 left in the first quarter.

The score was Cook's 45th career touchdown at Florida State, breaking the school record of 44 held by former running back Greg Allen (1983).

Aguayo redeemed himself on Florida State's third drive by hitting a 22-yarder to put Florida State up 10-0 with 13 seconds gone in the second quarter.

The Gators finally got on the board with 8:19 left in the second quarter after a 16-play, 54-yard drive was capped by a 38-yard field goal from Pinerio to trim Florida State's lead to 10-3.

Aguayo had a chance to make it 13-3 with under a minute left before halftime, but his 44-yard field-goal attempt was blocked, sending the Seminoles to the locker room ahead by seven. Aguayo was benched after that miss and backup kicker Logan Tyler handled kicking duties the remainder of the game.

The higher-ranked team has now won 11 of the last 12 meetings between these two in-state rivals. The only upset, so to speak, also went Florida State's way: Last year when the No. 13 Seminoles beat the No. 12 Gators at Ben Hill Griffin Stadium in Gainesville.

"Jimbo Fisher's put a hell of a program together," McElwain said. "He's got some really good players and they play the game the way it should be. My hat's off to what he has done here and what he has built."

NOTES: Florida State lost a Seminoles legend this week when former two-time All-America defensive back Monk Bonasorte died after a long battle with brain cancer. Bonasorte, who served as the school's senior associate athletic director, was honored with his No. 42 jersey in two ways Saturday night: The hash marks at the 42-yard line on both sides of the field were painted black, and Florida State players work "MB42" decals on their helmets. In Bonasorte's final game against Florida in 1980, he was key in the Seminoles' 17-13 win with nine tackles and three pass breakups. ... Florida, which still has one game left in the SEC Championship next week against Alabama, is the lowest-ranked defending SEC champion since the conference created a title game in 1992. The Gators were ranked No. 23 when they clinched the SEC East title with a 16-10 win against LSU last week. ... Florida State sophomore running back Dalvin Cook was named a finalist for the Doak Walker Award this week -- an honor given to the nation's best running back. Florida State has never had a Doak Walker Award winner. Cook came into Saturday with 4,166 career rushing yards and is the school's first 4,000-yard rusher. ... The announced attendance for Saturday night's game was 78,342.