Clarke ended with 18 points, while Mike Washington posted 22 points and 11 rebounds for the Razorbacks (10-11, 3-3 SEC), who had lost six of seven before winning their last two contests.
Marshawn Powell chipped in 19 points for the victors.
Murphy Holloway logged 19 points and 17 rebounds for the Rebels (16-5, 4-3), who had a three-game winning streak snapped. Chris Warren scored 17 points, and Eniel Polynice donated 15 points, seven boards and six assists in defeat.
This game was originally scheduled for Saturday but was moved due to inclement weather.
Ole Miss led 39-34 at halftime but came out cold in the second half. Powell scored eight points during a 13-6 stretch that gave Arkansas a 47-45 lead four minutes in.
The Rebels answered with eight of the next nine points to take the lead back, but the visitors quickly tied it at 55-all on Washington's free throw with just over 11 minutes to play.
It was a one-possession game until the final minutes, as Warren drained a three to tie things at 71-all with four minutes on the clock.
Clarke then hit the go-ahead trifecta, and Ole Miss followed with six consecutive misses from the floor.
Washington's two free throws preceded a Holloway bucket with 1:04 remaining for a 76-73 difference.
After Powell missed a three, Ole Miss' Terrico White missed the front end of a 1-and-1 with 29 ticks left.
Clarke's four straight makes from the charity stripe secured the outcome.
Ole Miss had won 13 of 14 home meetings against Arkansas since 1996-97...This was Arkansas' first true road win of the season.