The early lead was more than adequate for LSU starting pitcher Brian Wilson, who was lifted after six innings of work. He allowed two runs on seven hits to improve his record to 5-2 on the season.
Georgia starter Sean Ruthven (2-3) took the loss after giving up the Tigers' first eight runs in 2 2/3 innings.
The Tigers meet the Bulldogs again Saturday at 4 p.m., when the Tigers will look to win their sixth consecutive SEC series dating back to last season.
Hill started the scoring for the Tigers with his first double of the night, extending his hitting streak to ten games on his 21st birthday.
Ivan Naccarata followed with an RBI double to score Hill and extend his hitting streak to 19 games.
With runners on the corners, Clay Harris singled to left to score Naccarata for a 4-0 LSU lead.
Quinn Stewart hit an infield single that scored Gill, and Ruthven finally recorded his first out by striking out Ryan Patterson. A grounder to third from Liuzza accounted for the final LSU run of the inning.
Patterson redeemed himself for the strikeout in the third inning with a solo homer, his team high fifth of the year, and Liuzza followed with his home run.
Georgia (14-7-1, 0-4) plated its first run in the fourth and added two runs in the seventh off of LSU reliever Greg Smith to make the score 8-4. Billy Sadler entered the game and held the Bulldogs to one run while striking out five.
Hill plated the last two LSU runs with a double in the eighth inning.
Jordan Faircloth pitched the ninth inning for LSU and retired the Bulldogs in order with the help of two strikeouts.