Guard Cade Davis, as he has in recent weeks, led the way again with a 24-point scoring burst on 8-for-13 shooting.
And this time, several Sooners followed suit.
Three others finished in double figures, as guards Carl Blair, Steven Pledger and Cameron Clark netted 14, 10 and 10, respectively.
On the other side, they limited Baylor star guard Lacedarius Dunn to just 11 points on a miserable 3-for-14 performance from the field.
Because of that, the Sooners were able to surrender 21 points to forward Quincy Acy and 13 to forward Anthony Jones.
But that just wasn't nearly enough to overcome OU's huge first half lead.
The Crimson and Cream, a seven-point underdog coming into the contest, trailed 13-9 before using a 30-9 run to build a 17-point intermission lead.
And after leading 39-22 at the break, they never let the Bears crawl to closer than 16 again.
In fact, the Sooners led by as much as 25 when forward Tyler Neal hit a couple of free throws at the 3:52 mark.
With the win, Capel's job certainly does become that much more secure, and the Sooners will live to fight another day, as they'll face No. 2 seed Texas at 6 p.m. tomorrow.
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Amidst speculation that head coach Jeff Capel may be on his way out, the 10th seeded Sooners came out and smashed the No. 7 seed Baylor Bears 84-67 Wednesday night in Big 12 Tournament First Round action at the Sprint Center in Kansas City, Mo., putting a huge dent in those rumors.
The Sooner guard led the way with 24 points.