After trailing by as many as seven points in the first half, Arkansas, which has now won seven of eight games overall, rallied to go up 44-37 at halftime.
The Razorbacks then pushed their lead to 60-45 following an inside basket from Alandise Harris midway through the second half.
Gaines' fifth 3-pointer of the game brought the Bulldogs back to within seven points at 60-53, and they later closed to within 65-60 after free throws by Gaines.
Arkansas, however, went back up 70-60 after a jumper by Mardracus Wade and a 3-pointer by Ky Madden -- putting the game out of reach for Georgia.
Clarke's previous career high of 20 points came against Sam Houston State in 2012. He had scored 16 points three times this season.
Georgia, which defeated Arkansas in overtime on Jan. 18, led by as many as seven points in the first half -- thanks to a remarkable shooting effort that saw the Bulldogs hit 13 of their first 16 shots.
Gaines led the way, connecting on his first five shots -- including four 3-pointers -- and finishing with 14 points in the first half.
After Nemanja Djurisic's inside basket put Georgia up 35-27, however, the Razorbacks -- fresh off their first win at Kentucky in 20 years less than 48 hours earlier -- surged ahead.
After trailing 35-28, Arkansas went on a 16-2 run to close out the half.
Clarke started the run with a 3-pointer, and he ended it in athletic fashion -- skying to grab an alley-oop pass from Qualls and laying it home over Gaines for a three-point play. His free throw after the basket put the Razorbacks, who shot 14 of 24 (58.3 percent) in the first half, up 44-37 at halftime.
Clarke had 15 points in the first half, one off his previous season high of 16 points. He topped that mark with a free throw in the second half to put Arkansas up 52-42, and he hit four free throws in the final minute to earn his career-best effort.
After starting the half 13 of 16 from the field, Georgia hit just one of its final seven shots and finished 14 of 23 (60.9 percent) from the field.
The Bulldogs hit just 8 of 28 (28.6 percent) shots in the second half.