"I had a chance to tip it, and it was Kobe time," Udoh said, invoking the name of Los Angeles Lakers star Kobe Bryant after making his third game-winning shot of the season. "Thank God, because if we had lost we would have been sad."
Bears coach Scott Drew was far from sad as he punched the air over and over after Udoh's latest big play.
"We won it the way we wanted -- with rebounds and defense," said Drew, who evened his record at Baylor at 100-100 in his seventh season. "We know how important the boards are."
The Bears (10-5, 6-4 Big 12) had led from the opening minute before Missouri took a 62-61 lead with 47 seconds left on Kim English's breakaway layup and free throw after an intentional foul on LaceDarius Dunn.
But English missed the second free throw and J.T. Tiller misfired on the following possession. Baylor's Anthony Jones grabbed the rebound and Dunn was fouled on a fast break with six seconds left.
Dunn made the first free throw to tie it, but he missed the second. Baylor's Quincy Acy grabbed the rebound and took a fadeaway that bounced off the rim. Dunn's putback was too strong, but Udoh went up between Tiller and Justin Safford for the game winner.
"Ekpe doesn't mind having a lot of pressure on him, and he performs well under it," Drew said.
Point guard Tweety Carter called his teammate "special."
"Throughout the game he didn't score like he wanted to, but he stayed with it and kept playing defense for us," said Carter, who had 14 points. "You never know when the ball is going to be in your hands."
English's desperation 3-pointer from just inside halfcourt bounced off the rim at the buzzer.
"There were two or three tips and it looked like the clock was moving in slow motion," Missouri coach Mike Anderson said of the final scrum. "But we have no one to blame but ourselves, and I'll take the blame on that. We just came up a little short, but it wasn't because of effort or desire."
Zaire Taylor led Missouri (18-7, 6-4) with 15 points.
Dunn finished with 17 points, while Acy added 12 points and 11 rebounds for the Bears.
Udoh, who made the game-winning shot in Wednesday's 55-53 victory at Nebraska, had six points and 10 rebounds. He had three blocks to give him 100 this season, breaking Brian Skinner's school season record of 98.
Dunn's tying free throw was Baylor's first point since he made two free throws with 5:39 left to push the lead to 61-56. That lead disappeared when Tiller drilled a 3-pointer with 1:52 remaining and Dunn fouled English on the breakaway.
"I tried to foul him before he got it up on the rim," Dunn said. "But unfortunately, him being a great player, he got it up. We just had to put that behind us."
English and Safford both had 13 points for the Tigers.
Baylor controlled the backboards and tempo for most of the first half, taking a 38-32 lead behind 14 points from Dunn. English sparked a 9-3 run in the closing minutes of the first that kept the Tigers within range.