Georgia, already motivated to make up for a loss at Mississippi State last season, played as if it was inspired by an exchange of taunts before the game. The teams had to be separated at midfield at the end of pregame warmups.
Georgia took a 14-3 lead in the first quarter and led 21-3 at halftime.
Murray had an uneven performance. He completed 13 of 25 passes for 160 yards with two touchdowns but had three interceptions to match his total for the first four games
Crowell, the freshman tailback, did not score but topped 100 yards for the third time in three SEC games. One week after setting career highs with 30 carries for 147 yards in Georgia's 27-13 win at Mississippi, Crowell again was the most consistent offensive threat for Georgia.
Mississippi State was held to a 42-yard field goal by Derek DePasquale before finally reaching the end zone when Darius Slay returned an interception 72 yards for a touchdown midway through the fourth quarter.
Relf completed 19 of 31 passes for 157 yards and two interceptions. Vick Ballard was held to 23 yards rushing on eight carries.
Big plays on special teams set up Georgia's first two touchdowns.
A shanked 11-yard punt by Baker Swedenberg gave Georgia the ball at Mississippi State's 22 later in the opening quarter. Murray's 6-yard pass to Malcolm Mitchell gave Georgia a 14-3 lead.
Murray's second interception, by linebacker Cameron Lawrence, gave Mississippi State the ball at the Georgia 28 with 3:34 remaining in the half. Georgia's defense answered when Relf's pass bounced off receiver Chris Smith's hands and was intercepted by cornerback Sanders Commings.
Georgia took the ball at its 19 and, with Crowell doing most of the work, moved 81 yards on eight plays. The drive ended with Carlton Thomas' 7-yard scoring run.
Mississippi State coach Dan Mullen alternated quarterbacks in the third quarter. Dylan Favre, the nephew of former longtime NFL quarterback Brett Favre, took over for Relf for the first series of the second half before Relf returned the following possession. The two then shared Mississippi's third possession.
Favre threw passes, both incomplete.
Arceto Clark dropped a pass from Relf when hit by Brandon Boykin late in the third quarter. Commings recovered the fumble, setting up Blair Walsh's 18-yard field goal.
Tensions rose at the end of pregame warmups when Mississippi State's players gathered on the big painted ''G'' which stretches almost 20 yards at midfield.
Georgia players, who apparently felt offended the visitors took their normal gathering spot, crowded around the Mississippi State players. Coaches and officials quickly rushed to separate the players, but not before players on both sides pointed and taunted. An official was knocked down as he tried to escort the Mississippi State players off the field.
Georgia coach Mark Richt was seen having an animated discussion with the officials before he joined his players in the locker room.
At the end of the game, Georgia players quickly rushed to midfield, briefly bouncing up and down on the logo before exchanging handshakes with the Mississippi State players.
Georgia backup running back Ken Malcome, who told Richt on Wednesday he planned to transfer but was accepted back on the team on Thursday, did not play.