Travis Leslie scored 21 for the Bulldogs (14-16), the No. 6 seed in the SEC East Division.
Georgia took a 43-32 lead immediately after halftime on a 3-point play by Jeremy Price.
Arkansas' Mike Washington made all four free throws on back-to-back trips to the charity stripe to cut the Bulldogs' lead to 52-49 with 10:22 left. The Razorbacks (14-18) continued to threaten in the second half but never pulled any closer.
The Bulldogs grabbed 17 offensive rebounds, nine more than Arkansas, and turned them into 19 second-chance points.
Washington finished with 20 points and Courtney Fortson added 16.
The Bulldogs will face the East's No. 2 seed, No. 20 Vanderbilt, on Friday.
(This version CORRECTS APNewsNow. Georgia 77, Arkansas 64. corrects Georgia offensive rebounds to 17)