Dunn became the second Baylor player to surpass 2,000 career points, while Quincy Acy added 15 points and a game-high eight rebounds for the Bears (12-3 overall, 2-0 Big 12 Conference).
Steven Pledger led the Sooners (8-8, 0-2) with 17 points, and Cameron Clark added 16.
The Sooners were 14-0 on the Bears' home court and 26-0 against them in Big 12 play before Baylor swept the series last year.
The Sooners, who lost their last nine Big 12 games last year and this season's league opener at Texas A&M, have dropped 11 straight conference games. A loss at No. 12 Texas on Saturday would extend the streak to 12, Oklahoma's longest since losing 15 straight Big 6 contests in 1930-31.
Dunn scored on a drive with 17:07 left to crack the 2,000-point barrier. The senior has 2,009 points, leaving him 180 behind Terry Teagle on the school's all-time list and 247 behind all-time Big 12 leader Andre Emmett of Texas Tech.
Baylor never trailed, but OU kept it close for most of the second half as Pledger hit four of six shots from 3-point range.
Baylor jumped to a seven-point lead in the opening minutes and was in control until the final moments of the first half behind 12 points from Jones.