Murray shook off a pair of first-half interceptions, including one returned for a touchdown, and passed for 427 yards also a Bulldogs bowl record against the nation's top-ranked passing defense. He was the game's most valuable player on the way to earning his first bowl victory at Georgia.
Georgia (12-2) also reached 12 wins for the third time in school history.
"I don't know what it's like to head into an offseason with a win," Murray said. "It's a great feeling to get a win. It's great for the seniors, who have meant so much to this team. They've done a great job of leading this team the whole season.
"To get 12 wins ...that's something special."
Nebraska (10-4) lost its third consecutive bowl game, and finished the season with two straight woeful defensive performances. The Cornhuskers lost the Big Ten championship game 70-31.
The Cornhuskers led 24-23 at the half but committed two of their three turnovers in the final 30 minutes.
Taylor Martinez had two interceptions and two touchdown passes for Nebraska, and Rex Burkhead rushed for 140 yards in his final college game.
But Nebraska coach Bo Pelini said the efficiency of Murray and Georgia on third down (finished 12 for 17) was too much to overcome.
"I thought the plan was good," Pelini said of his team's defensive scheme. "Third down hurt us, obviously. When were in position, it was man on man down the field. We needed to make some of those plays and we didn't. And, you know, again, that cost us a football game."
Nebraska drops to 12-7 against SEC opponents in bowl games.
Trailed by questions about his team's focus following its narrow loss to Alabama in the SEC championship game, Georgia coach Mark Richt said Tuesday was also about a team that finished 5 yards shy of a BCS title game-berth finding closure.
"We wanted to win this game to prove to ourselves that we are one of the better teams in the country," Richt said. "I think our guys did a good job of sucking it up when they were tired...But when you make a big play here and there, it gives you a little more energy as well...We made enough big plays at the right moment."
Nebraska's offense finished with 443 total yards, but the Bulldogs defense was stingy when it needed to be.
They sacked Martinez five times, with junior All-American linebacker Jarvis Jones notching two. Damian Swann had both Georgia interceptions.
With his two sacks Jones set a single-season record for with 14.5 sacks for the season. He will now decide in the coming days whether or not to enter the NFL draft.
"I think our coaches did a great job of halftime adjustments and got us out there adjusting to what they were calling and got us players honed in," Jones said.
No. 6 Georgia 45, No. 23 Nebraska 31
Georgia 16 7 8 14 45
Nebraska 14 10 7 0 31
Geo • Safety, 11:39.
Geo • Lynch 29 pass from Murray (Morgan kick), 7:54.
Neb • Turner 14 pass from Martinez (Maher kick), 4:42.
Neb • Compton 24 interception return (Maher kick), 4:15.
Geo • King 75 pass from Murray (Morgan kick), 4:04.
Geo • Gurley 24 run (Morgan kick), 10:33.
Neb • FG Maher 39, 8:48.
Neb • Burkhead 16 pass from Martinez (Maher kick), 4:43.
Neb • Burkhead 2 run (Maher kick), 9:42.
Geo • Conley 49 pass from Murray (McGowan pass from Murray), 7:26.
Geo • Marshall 24 pass from Murray (Morgan kick), 14:52.
Geo • Conley 87 pass from Murray (Morgan kick), 11:03.
Attendance • 59,712.
First downs 23 26
Rushes-yards 38-162 52-239
Passing 427 204
Comp-Att-Int 18-33-2 16-27-2
Return Yards 89 42
Punts-Avg. 3-39.0 4-34.0
Fumbles-Lost 0-0 1-1
Penalties-yards 7-76 8-69
Time of Possession 27:33 32:27
Rushing • Georgia, Gurley 23-125, Marshall 8-36, Murray 4-3, King 1-0, Team 2-(minus 2). Nebraska, Burkhead 24-140, Abdullah 7-48, Martinez 20-46, Heard 1-5.
Passing • Georgia, Murray 18-33-2-427. Nebraska,
Receiving • Georgia, King 3-104, Scott-Wesley 3-67, McGowan 3-40, Marshall 3-39, Lynch 3-37, Conley 2-136, Gurley 1-4. Nebraska, K.Bell 4-60, Burkhead 4-39, Turner 3-22, B.Cotton 2-69, Enunwa 2-11, Reed 1-3.