Following a Nebraska punt, Murray then hit Chris Conley for a short pass in space over the middle. Conley outran the Cornhuskers defenders for an 87-yard score.
That play came after a 49-yard touchdown catch by Conley that helped Georgia tie the game in the third quarter.
Nebraska clung to a 24-23 lead at the half, taking back the advantage late in the second quarter via a 16-yard strike from Martinez to Burkhead.
After a pair of early turnovers, Murray seemed to be getting Georgia's offense back on track, as the Bulldogs punctuated a four-play, 38-yard drive with a 24-yard touchdown run by Todd Gurley to make it 23-17.
Both Bulldogs' turnovers came via Murray interceptions as the nation's top-ranked passing defense crowded Georgia's receivers and disguised their coverage schemes.
Gurley helped open things up, though, rushing for 81 yards in the opening 30 minutes.
Nebraska also allowed Georgia's defense three sacks, which thwarted some promising Cornhuskers drives.
"Their guys just made plays on stuff," Nebraska senior linebacker Will Compton said. "Our guys were there but, yeah, I mean they made more plays than we did at the end of the day."
Nebraska's defense didn't need long to force the game's first turnover, picking off a Murray pass on Georgia's opening drive of the game.
The Cornhuskers went three-and-out on their first offensive touch, and were forced to punt.
But that attempt by punter Brett Maher was blocked by the Bulldogs' Shawn Williams. There was a scramble for the ball in the end zone, but it trickled out of the back for a safety.
The Bulldogs then went up 9-0 their ensuing possession following the free kick, capping an 80-yard drive with a 29-yard touchdown pass by Murray to Arthur Lynch.
Nebraska's offense finally got going on its next touch, responding with a 14-yard touchdown pass from Martinez to Jamal Turner.
The Cornhuskers' defense then made with 14-9 when Compton came up with their second interception in the half on Murray and returned it 24 yards for the score.
"I'm real proud of Aaron and job he did," Richt said. "(He) had a couple of things go not exactly the way he wanted them to go. Had a couple of picks early. Just hung in there, very resilient and finished."