The Hilltoppers (4-2) opened the game with an emphatic dunk by Jeremy Evans, which set the tone for an intense game.
The game stayed close with the Bulldogs (5-2) gaining the largest lead of the game at 22-14 with 7:08 left in the first half. Georgia led 38-35 at halftime.
Western Kentucky held a one-point lead at 61-60 with 1:33 left in the game and built a 66-60 cushion. The Hilltoppers sealed the victory with free throws from Slaughter, Sergio Kerusch and Anthony Sally.
The game marked another return to Diddle Arena for Georgia coach Dennis Felton, who coached five seasons (1998-2003) at Western Kentucky and led the Hilltoppers to three NCAA tournament appearances. Felton has coached two games in Bowling Green for Georgia under the teams' four-year playing contract.
"I thought that was one hell of a college basketball game," Felton said. "I was hoping that it would be because Western Kentucky is playing fabulous basketball right now and we're a very young team, five freshman and four sophomores, and this is clearly our first opportunity like this of this season to play in this type of atmosphere."
Hilltoppers coach Ken McDonald was on the same staff with Felton under Rick Barnes at Clemson, and spent five seasons with Felton at Western Kentucky and one at Georgia.
"It got emotional after the game," McDonald said. "I didn't think it would. But Dennis has meant a lot to my career and I wish him luck, the class act that he is. ... I think they're going to go on to have a really good year, I really do. I think we are kind of both teams that are kind of evolving."
The first half was a two-man show between Slaughter and Georgia's Terrance Woodbury, who each scored 16 points in the first half. Woodbury finished with 18 points.
Kerusch added 13 points for the Hilltoppers and Evans had 10.
Trey Thompkins was the only other Bulldog in double figures with 10.
Georgia shot 41 percent (25-of-60) for the game, including 51 percent in the first half. Western Kentucky (4-2) shot 35 percent (22-of-62) from the field.