The top-seeded Aggies (49-7) took the lead on consecutive singles by Jamie Hinshaw, Holly Ridley and Erin Glasco to start the second inning. Macie Morrow added a one-out single to make it 2-0.
Kelsey Spittler added an RBI single, Morrow scored on a wild pitch and Gibson added a run-scoring groundout as the lead swelled to five in the fourth inning.
"It's just great to finally get that monkey off our back," Aggies head coach Jo Evans said. "We haven't played well at this tournament and I thought we came out this weekend and looked really good."
Gibson (33-1) picked up her 16th shutout of the season, striking out six.
Nebraska (25-27) came into the tournament as the last place team in the conference and became the first No. 10 seed to reach the championship game. A win would have given the Cornhuskers an automatic bid to the NCAA tournament.
Molly Hill (15-17), the winning pitcher in Nebraska's upsets of Kansas, second-seeded Oklahoma and Texas Tech, gave up five runs on 10 hits for the Cornhuskers.