Clarke was 6-for-15 and 4-of-11 from 3-point range to lead the Razorbacks (14-13, 2-12 Southeastern Conference) to their first win since late January.
Freshman forward Trey Thompkins had 20 points and eight rebounds to lead the Bulldogs (11-18, 2-12). Terrance Woodbury and Dustin Ware added 10 points apiece. Ware also led the team with six assists.
Sunday's game was a rematch of the 2008 SEC Tournament championship game, won by the Bulldogs. The win was Arkansas' first since a Jan. 29 win over Alabama. The Razorbacks lost eight in a row in February. Georgia came into Fayetteville after beating Vanderbilt on Wednesday.
With members of Arkansas' 1994 national championship team in attendance, Arkansas took the lead with 11:21 left in the first half and never lost it.
Georgia has two more games before the SEC Tournament starts next week. The Bulldogs play at Kentucky on Wednesday and get South Carolina at home Saturday to close out the regular season.