Alex Bregman had two of the eight hits for LSU (15-1), which scored three runs over the first three innings to take a 3-1 lead.
From his shortstop position, Bregman also caught the final out of the game, with Nebraska's Austin Darby on first base. Bregman made a nice catch running toward left field on a ball hit by Austin Christensen, whose bases-loaded single in the seventh inning made it a 3-2 game.
In supporting Godfrey (3-0), Conner Hale had two RBIs. For the Classic, the Tigers' third baseman reached base eight times in 12 plate appearances, delivering five hits -- including a home run -- as well as five RBIs.
Bregman scored twice on Sunday, and Jake Fraley and Andrew Stevenson also scored for LSU -- which defeated Houston 4-2, on Friday and beat Baylor, 2-0, on Saturday.
Nebraska scored in the first inning on Ben Miller's two-out single that plated Luis Alvarado. But Miller was out at first base after stumbling while rounding the base and trying to return to the bag.
Baserunning miscues derailed Nebraska (7-6). Tanner Lubach, who had two of Nebraska's nine hits, led off the second with a double before being doubled off third, completing a 6-5 double play. Steven Reveles singled leading off the sixth, but was subsequently picked off first base.
"This isn't the first time we've played a good baseball team, and it's not the first time we've seen a team hit the ball hard," Nebraska coach Darin Erstad said. "We gave ourselves an opportunity to win and, again, we were on the short end of making plays. We had too many mistakes on the bases. That's my fault."
Richard Dean is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.