Trailing by one point just moments after guard Steven Pledger briefly gave them the lead with a huge triple, Osby was freed out top but couldn't hit a potential game-winner with a few ticks left.
OU was then forced to foul, where Arkansas made a couple free throws and forward Tyler Neal's half court heave went wide after that, allowing the Razorbacks to escape with an 81-78 victory at Bud Walton Arena after squandering an 11-point halftime lead.
Pledger's three made it 78-77 with 22 seconds to go, but Arkansas guard B.J. Young's runner in the lane with 14 seconds remaining became the eventual game-winner.
While Young managed double figures, it was forward Marshawn Powell that torched them for most of the night.
He finished with a game-high 33 points while converting 11-of-17 shots and also bringing down six boards to go along with five assists.
Guard Mardracus Wade added 10.
The Sooners fought an uphill battle most of the way after taking an early 6-2 lead.
They trailed 31-22 before closing the gap to 41-38 at intermission.
In the second half, the Hogs extended their lead to as much as 11 twice before OU came storming back.
Seemingly every time OU got within striking distance, Arkansas had an answer.
But still, the Sooners hung around and long enough for what looked like the shot that finally put them over the hump when Pledger busted from long range late.
Not to be.
Along with Osby, who came off the bench for his first time as a Sooner, forward Amath M'Baye and Pledger both finished in double figures with their 14 and 12, respectively.
The Sooners had a 41-36 edge on the glass and outshot the Razorbacks 55.4 percent to 52.6 percent, but turned it over 17 times.
This loss snaps a three-game winning streak and sends OU (6-2) into an 11-day break before facing off against another SEC foe, Texas A&M, at 1 p.m. CT Dec. 15 in the All-College Classic in Oklahoma City.