Page had made 93 percent of his free throws in Big 12 Conference play this season but his miss allowed Nebraska a chance to win it. But Lance Jeter lost the ball in the lane while being defended by OSU's Matt Pilgrim and the Cornhuskers did not even got a game-winning shot off before the buzzer sounded.
OSU improves to 19-12 overall, while Nebraska saw its NCAA tournament hopes dashed with the loss and fell to 19-12.
The Cowboys, who are now 9-0 alltime in first-round Big 12 tourney games, advance to Thursday's quarterfinals where they will face No. 1 seed Kansas (29-2) at 11:30 a.m. The Jayhawks defeated the Cowboys 92-65 on Feb. 21 in Lawrence, Kan.
"I'm proud of our basketball team. It's always great to win but it's great to win when your whole team contributes," said Cowboys head coach Travis Ford.
"I thought we got off to an incredible start. I thought our defense the first eight to 10 minutes of the first half was as good as you could possibly play defense, not just as well as we've played but I don't know if (anybody) could play better defense than we played the first 8 to 10 minutes," Ford added.
The Cowboys didn't look like a team that was just 6-10 in Big 12 play and finished in ninth place in the league during the game's first 10 minutes. OSU made 8 of its first 11 shots, including going 5-for-5 from behind the three-point line, and played stifling defense on the Cornhuskers to take a 25-11 lead, and was on a pace to score 100 points.
But Nebraska clawed back to within 30-21 at halftime and pulled ahead 39-38 on Brandon Ubel's trey with 11:20 remaining in the game.
The Cornhuskers appeared to be on their way to the victory, and possibly getting off the proverbial NCAA bubble, when Caleb Walker's basket gave them a 48-44 lead with under six minutes to play.
But Page drained a pair of three-pointers on consecutive possessions to put the Cowboys back on top, 50-48, with 3:57 on the clock and it was a battle the rest of the way.
Nebraska trailed 51-50 when it fouled Markel Brown, a 56 percent foul shooter, with 34.6 seconds left in regulation. But the OSU freshman calmly sank both ends of the one-and-one to increase the margin to three.
The Cornhuskers scored an easy basket on their next possession and then had to foul Page with 16 seconds remaining. But the 93 percent free-throw shooter missed, allowing Nebraska a chance to win in regulation before Jeter committed the game's final turnover.
"I was definitely feeling horrible after that last free throw but I had confidence in my teammates that that last play we were going to come down and get a stop, and that's exactly what we did," said Page, who scored a team-best 16 points. "Jeter came down and got a switch on Matt Pilgrim and he did a good job of staying in front of him, and took the ball away and we came up with the loose ball. We were just fortunate."
The Cornhuskers scored just four points and made only one basket in the final six minutes of the game as the Cowboy defense stepped up when needed.
"We talked so much during the timeout that we've got to find the energy level and we've got to find that mentality to just get the ball back from a turnover or a rebound, not through the net," said Ford. "What I've talked about all year long is if you can make a few threes, make a few shots, it fuels you on the other end.
"Those last six minutes what did they come off? Keiton Page's two threes. It fuels your team. I've seen it a million times, you have a big lead, and a nine-point lead is a lot on Nebraska, and for us to come out and lose that lead ... teams just quit, they get deflated ... then all of a sudden we get the lead back and it just re-energized us. I thought getting the lead back was crucial, and we played very well as far as getting stops."
Marshall Moses was the only other Cowboy to score in double figures with 10 points but Matt Pilgrim also came up big – other than the final stop on Jeter – with 12 rebounds against the bigger, taller Cornhuskers (6-10 Brandon Ubel, 6 rebounds; 6-11, 320-pound Andre Almedia, 5 rebounds, and 6-11 Jorge Brian Diaz, 3 rebounds).