Washaun Ealey led Georgia with 17 carries for 123 yards and a touchdown. Caleb King, who normally shares carries with Ealey, served the first game of his two-game suspension following his arrest for failing to pay a speeding ticket.
Georgia (3-4 overall, 2/3 Southeastern Conference) took its second straight lopsided win after four straight losses. The Bulldogs beat Tennessee 41-14 last week.
Georgia introduced its new mascot, Uga VIII, a 13-month-old white English bulldog, before the game.
Vanderbilt (2-4, 1-2) suffered its 15th loss in the last 16 games in the series.
Blair Walsh kicked two field goals for Georgia but missed from 31 yards in the fourth quarter to keep the Bulldogs from taking their largest margin of victory in the series. Georgia beat Vanderbilt 45-0 in 1976.
Murray, a freshman, completed 15 of 24 passes for a career-high 287 yards and two touchdowns with no interceptions. He had scoring passes of 4 yards to Kris Durham and 48 yards to A.J. Green. Durham had four catches for 112 yards.
Murray has 12 TD passes and only three interceptions this season.
Murray and other starters were pulled late in the third quarter. Hutson Mason took over at quarterback.
Thomas, a sophomore, had four carries for 40 yards, including scoring runs of 15 and 9 yards.
Larry Smith completed 5 of 14 passes for 70 yards with an interception for Vanderbilt.
Jared Funk replaced Smith for the fourth quarter.
Georgia appeared unsettled in the opening minutes. The Bulldogs called timeouts before their second defensive and third offensive plays.
Fans booed when coach Mark Richt sent his field goal team onto the field on fourth and 1 at the Vanderbilt 16. The ball was snapped and Walsh kicked the field goal as Richt called timeout from the sideline -- Georgia's final timeout of the half.
Richt then sent his offense back on the field. Murray ran for the first down but Georgia eventually settled for a 32-yard field goal by Walsh.
Georgia had two apparent touchdowns overturned on reviews.
After an apparent completed pass from Smith to Mason Johnston and fumble by Johnston, linebacker Christian Robinson picked up the ball and ran about 40 yards into the end zone. Officials ruled a touchdown but the play was ruled an incomplete pass on review.
Late in the first quarter, Vanderbilt's Joey Bailey snapped the ball past Smith into the end zone. Georgia's Akeem Dent fell on the ball at the back of the end zone. The officials' touchdown call was changed to a safety on the review.
Thomas had a 15-yard touchdown run, Kris Durham caught a 4-yard touchdown pass from Murray and Walsh added a 25-yard field goal with 18 seconds remaining in the half for a 22-0 lead.
Thomas added a 9-yard touchdown run in the third quarter.
Sanders Cummings intercepted a pass by Smith with 5:35 remaining in the third quarter to set up Georgia's last touchdown, a 1-yard dive by Ealey.
Umpire Johnny Hibbett was helped off the field with 7:45 remaining in the third quarter with an injured left ankle. Line judge Terry Walters took over for Hibbett.