The Sooners opened up the game with stifling defense, holding the Bears without a field goal for the first 4:24 until junior guard Lacedarius Dunn hit a three from the left side.
That cut an early OU lead from six to one, but the Sooners responded with a nice run to build a double digit lead.
OU scored 11 of the game's next 12 points to lead 21-11 halfway through the first half.
But Baylor wouldn't let the Sooners extend that lead any further.
The Bears used a 16-5 spurt over the next six minutes to grab their first advantage of the game at 27-26, in large part because of a scoring surge by Dunn.
"We talked about how we needed to defend LaceDarius Dunn," Capel said. "I think LaceDarius is one of the best scorers in college basketball. I think he's one of the best shot makers."
And the rest of the first half was back-and-forth from there.
There were four lead changes in the final four minutes of the half, as Baylor carried a 36-35 lead into the intermission.
After OU tied it at 40 in the opening possessions of the second half, it was the Bears who started to take control, especially on the defensive end where they held OU to only 25.7 percent in the second half.
"[Defensive intensity] was our key to the game," said Baylor head coach Scott Drew. "It started with Tommy-Mason Griffin who has been playing as good as any guard in the country. Tweety [Carter] did a phenomenal job on him, and it is obviously a team effort whenever you are guarding a great player like him. Our bigs did a good job helping out on ball screens. I am just proud of the defensive effort from our guys."
With that strong defensive presence, Baylor mounted an 11-3 run to lead 51-43 with 12:38 remaining.
But this time, the Sooners managed a rally of their own from eight points down to get back within striking distance.
And senior forward Ryan Wright hit a pair of free throws to finally put them over the top at the 6:56 mark, their first lead since a 33-32 advantage in the final two minutes of the first half.
From that point on, neither team could put the other away.
But in the end, the Bears simply made more winning plays.
The Sooners had a chance to get back within one or tie it up in the final 45 seconds, but they just couldn't hit a shot down the stretch.
"It's amazing when you look at our percentages shooting the basketball that we were actually in this game and had a chance to win late," Capel said. "We got good looks when we executed, but it was just one of those afternoons where we couldn't make shots."
Freshman forward Tiny Gallon led the Sooners with 23 points on 11-for-17 shooting, and Wright added 12.
Dunn led the way for Baylor with 21, and junior forward Ekpe Udoh had 20.