OKLAHOMA CITY -- TCU's Tyler Alexander was demoted to the bullpen after his last outing against Oklahoma State. Alexander, a freshman left-hander, showed he learned a big lesson from that experience.

Alexander threw his first career complete game, a four-hitter, and Dylan Fitzgerald hit a two-run single during a decisive four-run fourth inning and TCU beat Oklahoma State 7-1 on Sunday in the Big 12 Conference tournament title game.

"I don't want to understate it, because it was phenomenal what [Alexander] did," coach Jim Schlossnagle said. "Oklahoma State has a really veteran, physical, offensive team and he did a great job of just commanding all three pitches and throwing at the bottom of the strike zone."

In making its argument for a top-eight seed in the upcoming NCAA tournament, TCU (42-15) won its first team title — in either the regular season or postseason — in any sport since joining the Big 12 before the 2012-13 school year. The Horned Frogs have won 27 of their past 30 games, including four in a row in the conference tournament.

It's a long way from last year, when the Horned Frogs scuffled their way to a 29-28 mark and a seventh-place finish in their first season in the Big 12.

"These guys have earned it," Schlossnagle said. "Most of the guys on this team . had to go through a nightmare last year. It's not life or death, but it wasn't fun, especially for the standards this program has.

"I just like to see the smiles on their faces, because I know what great people they are. All those guys have been through a lot and I like seeing them rewarded, because they've earned it."

TCU and Oklahoma State (45-16) both are among the 16 teams that will host a NCAA tournament regional. Oklahoma State was the Big 12 regular-season champion, finishing a game ahead of TCU. With 45 wins, the Cowboys already have recorded their most wins in a season since 1999, when they reached the College World Series.

The difference Sunday was that while TCU had a fresh pitcher in Alexander, the Cowboys — who had to come through the losers' bracket — were playing their sixth game in five days and were almost out of effective pitching. By game's end, the Cowboys used sophomore outfielder Corey Hassel, who hadn't pitched since high school, to throw the eighth inning.

"At the end of the day, the value of staying in the winners' bracket showed itself," Schlossnagle said.

Alexander (9-3) established a tone early, as nine of his 10 first-inning pitches were strikes. He finished with four strikeouts and no walks and allowed only two baserunners past second base.

"I pitch best when I pitch ahead in the count," Alexander said. "That's a big part of me keeping my pitch count low."

Kevin Cron singled and scored on Jerrick Suiter's groundout in the second inning to give Texas Christian a 1-0 lead. Oklahoma State tied it in the top of the third when Tim Arakawa scored on a safety squeeze bunt single by Saulyer Saxon.

Oklahoma State starter Michael Freeman (2-1) walked the bases loaded with one out in the fourth before Fitzgerald singled up the middle to put the Horned Frogs up 3-1. Another run scored on a groundout by Keaton Jones and Oklahoma State catcher Bryan Case's second passed ball of the inning allowed Fitzgerald to score, making it 5-1.

In the fifth, TCU's Garrett Crain walked with two outs, stole second base and scored on a single by Suiter, who was named as the tournament's most outstanding player. Freeman, who entered having thrown 9.1 innings all season, lasted until leaving the game with a cramped hamstring in the sixth inning.

The Cowboys were trying to become the fifth team in Big 12 history to sweep both the regular-season and tournament titles. Oklahoma State's only Big 12 tournament title came in 2004, when the Cowboys beat Missouri 10-9 in 13 innings in the championship game.

"I'm very proud of our team," Oklahoma State coach Josh Holliday said. "I think what they accomplished in the last five days was significant. We played six games in five days, the most baseball we've played all year, and for the most part it was very high-end, quality baseball against elite opponents. It certainly prepared us for what lies ahead."