But fans were pressing toward the field, which is separated from the stands by an eight-foot stone wall. Some students jumped down, others were pushed. The crowd pulled down the goal posts, and in the 45 minutes or more it took police to restore order Saturday night, some fans were trampled as the crowd struggled to reach the exits.
At least 12 people were injured, including one who was airlifted to a hospital, in the chaos on the field after an emotional win in the heart of football country.
"Thousands of people stormed the field. You couldn't move, there were so many people," said Michael Authement, who heads the command post at emergency medical provider LifeNet EMS. "It was a nasty deal."
The field is not designed to allow huge crowds to get in or out. Narrow staircases on the north, south and west ends are the only ways to reach the field from the seating areas. There are two ramps on the east end, which has no seats.
To get back off the field, fans were crunched together and pushing to get their way to the exits.
The public address announcer had warned fans not to storm the field, but "we just laughed," said Alex Lillibridge, a 19-year-old freshman from Belton, Texas. Fans started jumping the wall in the last seconds of Oklahoma State's 44-10 win, and Lillibridge said that soon after he followed.
Some people said they were forced to jump because of the crush of fans.
"A girl pushed me over the wall," said 21-year-old Jennifer Payne, a junior from Stillwater. "Luckily, I didn't get injured, but I didn't have control of when I jumped off the wall. You just moved with the crowd."
Jerry Nevils, who was at the game but did not storm the field, said Sunday that the yellow-jacketed security force surrounding the field was no match for the "slow, steady avalanche" of Oklahoma State students and other fans.
"They weren't stopping them, not with the 20 or 30 people they had there," said Nevils, of Sapulpa.
Oklahoma State spokesman Gary Shutt said two people were airlifted to Oklahoma City for treatment, including one adult who had a medical problem well before the end of the game. Both were listed Sunday in guarded, stable condition.
Shutt said the university could not disclose the student's injuries because of health privacy laws but that he was "alert."
Eight people were taken to Stillwater Medical Center - including two who were having surgery Sunday on broken ankles. Three others were treated at the field, he said.
University President Burns Hargis praised medical personnel on Sunday night and said stadium security "did everything they possibly could."
"They've been tearing down the goal posts for 80 years," Hargis told the AP. "I wish we could have kept people in the stands, but once that many thousands of people start pouring onto the field, there's not a lot you can do."
Shutt said university's policy is to keep fans off the field, and that he heard fans booing the announcer's warning to remain in the stands.
"You couldn't put an army out there to keep that many people off the field, if that's where they're coming," Hargis said. "And even if you did, the fallout from that wouldn't be very desirable."
Still, the mood in Stillwater on Sunday was not of shock but excitement over what may be the football program's most successful season ever.
With their rout of No. 13 Oklahoma, the third-ranked Cowboys claimed their first-ever Big 12 championship, snapped an eight-game losing streak in the "Bedlam Series" against the Sooners and made a case to play for the Bowl Championship Series national title.
However, the Cowboys (11-1, 8-1 Big 12) were passed over for that honor when the BCS rankings were released Sunday night. Instead, two Southeastern Conference teams - Louisiana State and Alabama - were selected to play a rematch Jan. 9 in the title game.
The Cowboys have rarely been the first word in football in Oklahoma, where the Sooners boast seven national championships.
Getting pushed around in the crowd was worth it for Garrett Stone, 25, a recent OSU graduate who came in from Dallas to see the game.
"The thrill, the national exposure, doing so well this year and being able to potentially jump Alabama, the first Big 12 title, beating OU for the first time in eight years," he said.
Authement said the crowd was so big it took police at least 45 minutes to clear fans from the field at the university's Boone Pickens Stadium. The crowd of 58,141 was the fourth-largest crowd ever at Oklahoma State.
Shutt, the university spokesman, said he did not know if any of the injuries were related to the goal posts being brought down. He said the university does not use the form of collapsible goal posts that get laid flat on the ground after the game, but they do use a form that is easily dismantled.
Oklahoma State University police referred questions to the university. Stillwater police said they had a handful of officers at the game, and the Oklahoma Highway Patrol had no immediate comment.
Before reports of injuries emerged, Oklahoma State coach Mike Gundy said he left the field quickly when he saw fans jumping from the wall.
"When they started piling over, I got out of there as fast as I could. ... It was scary," he said.
He noted that in OSU's last game, a double-overtime loss at Iowa State on Nov. 18, it was the other team's fans who stormed the field.
"We almost got trampled by the other team. And now, we went the other way. It's ironic, and things happen for a reason. Don't know why," Gundy said.
The chaos struck a university that has been mourning the loss of women's basketball coach Kurt Budke and his assistant, Miranda Serna, who were killed last month in a plane crash along with the pilot and his wife. OSU and OU's marching bands performed "Amazing Grace" at Saturday's game to honor the victims.
The campus also was jolted Nov. 5 by the strongest earthquake in Oklahoma history. The magnitude-5.6 temblor struck Boone Pickens Stadium just as fans were leaving another football game.
Associated Press writers Bill Cormier in Atlanta and Jeff Latzke in Stillwater contributed to this report.