Armstrong threw for 163 yards and Ameer Abdullah ran for 122 yards with a touchdown for Nebraska (9-4), which had concluded the regular season with an ugly home loss to Iowa on Thanksgiving weekend.
"The way we do things at Nebraska, this is a team win," said Nebraska coach Bo Pelini at the trophy presentation. Pelini came under fire after the loss to Iowa.
Enunwa caught four passes for 129 yards in the victory and was named the game's MVP. The Cornhuskers improved to 25-25 all-time in bowl games and also snapped a three-game postseason slide, which included a 45-31 loss to Georgia in last year's Capital One Bowl.
Hutson Mason completed 21-of-39 passes for 320 yards with a touchdown and an interception for Georgia (8-5), which played without record-setting quarterback Aaron Murray. The senior suffered a torn ACL in the next-to-last game of the regular season.
Todd Gurley ran for 86 yards and caught seven passes for 97 yards with a score for the Bulldogs, who had a pair of chances to take the lead with late drives in the fourth quarter.
After Georgia's Marshall Morgan connected for his fourth field goal of the game, a 30-yarder with 6 1/2 minutes left in the third to make it 17-12, the Huskers faced 3rd-and-14 from their own one. Rather than play it safe, Armstrong dropped back in the end zone and found Enunwa alone downfield. He caught the ball near the 40-yard line and broke a tackle from Quincy Mauger before racing the rest of the way untouched.
Armstrong's next throw was intercepted by Shaq Wiggins at the Nebraska 39 and the Bulldogs finally reached the end zone after the turnover when Mason hit Gurley with a 25-yard touchdown pass on the first play of the fourth quarter.
Georgia reached midfield with its next possession before punting it away, then got the ball back at its own 20 with 7 1/2 minutes remaining. The Bulldogs quickly advanced to the Nebraska 22 thanks in part to a 48-yard pass from Mason to Michael Bennett, but soon faced 4th-and-2 and decided against a field goal with plenty of time left and two timeouts. Rantavious Wooten had a pass for a first down in his hands, but took a hard hit from Andrew Green and failed to hold on.
The Bulldogs quickly forced another three-and-out and again took over at their own 38 with 3:18 to play. A 29-yard pass to Chris Conley on the first play put Georgia back within striking distance, but the Bulldogs again faced 4th-and-3 at the 16 and tight end Arthur Lynch dropped a pass with 25 seconds left.
A slow first quarter featured five punts, but Georgia kicked a trio of field goals in the second and Nebraska's first touchdown came off a muffed punt by the Bulldogs as the Huskers grabbed a 10-9 halftime edge.
Morgan's first field goal, a 38-yard boot, came 4 1/2 minutes into the second quarter to give Georgia a 3-0 lead. The Huskers went three-and-out on their ensuing series, but Reggie Davis couldn't handle the punt and Nebraska needed just two plays to go 14 yards for a touchdown.
Enunwa brought down Armstrong's pass in the end zone from five yards away to give Nebraska a 7-3 edge. Morgan's 28-yard field goal on the next Georgia possession was answered by a 46-yard Pat Smith kick for the Huskers, but Morgan added a 38-yarder as time expired in the half.
Nebraska's Josh Mitchell picked off Mason on the third offensive snap of the second half and the Huskers needed seven plays to make it 17-9. An 18-yard pass from Armstrong to Enunwa put Nebraska inside the 20 and an interference penalty on a third-down incompletion set up Abdullah's 1-yard scoring run.
Nebraska's previous longest touchdown pass was a 95-yard toss from Fred Duda to Freeman White against Colorado on Oct. 23, 1965 ... Enunwa finished with 12 touchdown catches this season, breaking the Nebraska record of 11 set by Johnny Rodgers in 1971 ... Georgia fell to 27-19-3 in bowl games, including 2-1-1 in the Gator Bowl ... Nebraska has won each of its two appearances in the Gator Bowl, previously earning a 26-21 win over Clemson in 2009.