TALLAHASSEE, Fla. -- Last season ended on an ugly note for Florida State with an embarrassing and lopsided loss to Oregon in the Rose Bowl.

But on Saturday night, the Seminoles showed that was a distant memory.

No. 10 Florida State began the post-Jameis Winston era with a convincing 59-16 win over Texas State in the season opener for both teams.

With the Heisman-winning quarterback gone to the NFL, graduate transfer Everett Golson -- who joined the Seminoles this offseason by way of Notre Dame -- looked every bit as good as Winston did in his Florida State debut two years ago.

Golson completed 19 of 25 passes for 302 yards and four touchdowns, and running back Dalvin Cook -- who saw less than two weeks of practice time after returning from suspension -- didn't show any rust as he rushed for 156 yards and two touchdowns on 19 carries.

"Solid first game," said Florida State head coach Jimbo Fisher, who is now 6-0 in season openers at Florida State. "I liked what Everett did -- not just throwing the ball -- but how he managed the game and his communication. He did some nice things in that regard, and his throws were precise and accurate. He has a few things he needs to work on, but overall, good first game."

Texas State, meanwhile, was nearly shut out in the second half after scoring 10 points early and appearing like it would hang tough. But the Florida State defense was too rugged and the Bobcats, who joined FBS in 2011, are now 0-3 all time against programs from Florida.

Florida State's offense rolled up 636 yards compared with 300 yards for the Bobcats.

"I was proud of our guys. They fought hard. We were in decent shape at halftime and we didn't make any first downs in the third quarter and we couldn't get off the field," said Texas State head coach Dennis Franchione, who is now 2-5 in his storied college career against ACC programs. "The defense couldn't get a stop and it got away from us. Playing a team that's like this, that can't happen."

The Seminoles began to distance themselves early in the third quarter when Golson threw the first touchdown of his Florida State career to Travis Rudolph from 5 yards to put the Seminoles ahead comfortably at 28-10.

Golson then threw his second touchdown -- a 13-yarder to tight end Ryan Izzo -- to make it 35-10 with just over four minutes remaining in the third quarter. Izzo, who was making his first career start, replaced John Mackey Award winner Nick O'Leary at the position.

Golson threw his third touchdown pass just after the start of the fourth quarter -- a 14-yard dagger to Jesus Wilson, who led the team with three catches for 53 yards, to put Florida State well in front at 42-10.

Golson's fourth and final passing TD pass might have been his best -- a 55-yard bomb to Javon Harrison.

With the Seminoles ahead 49-10, Golson's night was done. And his debut a success.

Texas State quarterback Tyler Jones struggled most of the game, going 16 of 25 for 100 yards and no touchdowns. Jones had at least one passing score in his last 16 games -- the third-longest streak in FBS.

"I like the way our defense came out," said Florida State linebacker Terrance Smith, who was one of three Seminoles with seven tackles each. "We started fast and we executed the ball pretty well. But with it being the first game, we (also) have a lot to improve on."

Texas State running back Robert Lowe, who became the school's first 1,000-yard rusher a season ago, was hemmed in all game, carrying eight times for 13 yards. Jones led the Bobcats with 39 yards on 10 rushes.

Jones was replaced in the second half by Bobcats backup quarterback Connor White, who finished 10 of 17 for 68 yards and a late touchdown to receiver Chris French.

Golson, too, was replaced, but not until Florida State's final possession. Sean Maguire, who lost the starting job to Golson in fall camp, hit third-string running back Jonathan Vickers on a swing route out of the backfield for a 24-yard score.

Florida State kicker Roberto Aguayo capped the scoring with a 22-yard field goal with 2:18 left.

Florida State's defense under second-year coordinator Charles Kelly was put to the test but responded by forcing Texas State to punt on its opening possession. Florida State's offense then methodically marched 10 plays in 85 yards and capped it with a 1-yard dive into the end zone from Cook as the Seminoles struck first.

Aguayo, who holds the NCAA record for most point-after attempts without a miss, drilled his 150th consecutive career PAT to put Florida State ahead early 7-0.

Cook scored his second touchdown of the game late in the first quarter, finishing a three-play, 66-yard drive with a nifty 28-yard scamper.

Texas State scored the next 10 points -- with a 26-yard field goal from kicker James Sherman that was set up by a fake punt at midfield and then a 4-yard touchdown on the next drive by running back Chris Nutall.

Nutall's touchdown was set up after a muffed punt by Florida State punt returner Marquez White, who assumed the return role for the first time this season, on Florida State's 29-yard line. White was replaced on special teams after that.

"I was really disappointed by our special teams. We didn't field punts well, we didn't punt well and Roberto kicked the ball out of bounds twice on kickoffs," Fisher said. "Those are things we have to get ironed out very quickly."

Florida State added a score before halftime when backup running back Mario Pender scampered in from 1 yard to put the Seminoles ahead 21-10. Pender finished with 14 carries for 94 yards, and his score was set up by a 36-yard run by Cook.

Cook rushed 13 times for 122 yards in the first half, nearly outgaining Texas State's offense, which had 143 yards.

"It felt great to be back out there on the field with my brothers," said Cook, who was found not guilty of misdemeanor battery by a Tallahassee jury last week and immediately reinstated to the team.

Along with Smith, Lamarcus Brutus Terrell Lyons also had seven tackles each, and defensive back Derwin James recovered a fumble late in the game.

Texas State's Demetrius Woodard paced the Bobcats with seven stops and a sack.

NOTES: All Florida State and Texas State players wore decals on their helmets in honor of FSU coach Jimbo Fisher's charity, "Kidz1stFund," which is dedicated to the fight against the rare blood disease Fanconi anemia. Fisher's youngest son, Ethan, suffers from the disease and it's the third straight season Florida State's opponent has agreed to wear the decal in the Seminoles' opener. ... This was the first time Texas State had ever faced a nationally ranked opponent in its season opener, and the Seminoles' No. 10 ranking also represented the highest-ranked opponent the program has ever played. ... Two former Florida State standouts were inducted into the school's Hall of Fame during halftime: tight end Pat Carter (1984-87) and cornerback Tay Cody (1997-01). ... Florida State's game next week against South Florida -- scheduled to begin at 11:30 a.m. -- is the earliest kickoff in program history ... Saturday's game started after an hour-long weather delay due to lightning.