Bonner made 6-15 field goals and added five rebounds and three assists as she scored 17 for the Tigers.
Coach Nell Fortner's Tigers held the Aggies to 37 percent shooting while making 44.8 percent from the field, including 9-24 three-pointers.
Nine players scored for the Tigers, who got eight points off the bench from junior guard Joanna Clayden.
UC-Davis, which fell to 5-6, got 17 points from Heather Bates, who came off the bench to make 5-6 treys.
The Tigers led 38-28 at halftime as they shot 48.3 percent in the first 20 minutes.
For the game the Tigers blocked eight shots, six more than the Aggies. Senior Marita Payne got four blocks for the Tigers to go with five rebounds and six points.
Auburn struggled at the foul line, making just 8-20 while UC-Davis was 6-6. The Tigers, who have struggled on the boards at times this year, enjoyed a 40-31 rebound margin and had 13 turnovers, four less than the Aggies.
"UC Davis is a team that never quits so I felt the game was never over against a team that can shoot like they can," Coach Nell Fortner said. "DeWanna gave us a 20-point lead, which was important because you have to have that type of lead against them. We had six days off from practice over the holidays so I liked what I saw out there today."
Fortner had praise for her senior guard, too. "Brown is playing with tremendous confidence," Fortner said. "Her defense was already outstanding, but now she is starting to take pride in her shooting as well. This is her team and she is not afraid to take the tough shot anymore. We have needed her to step up into this role and she has done that."
The Tigers will play Loyola of Maryland at 9:30 p.m. CST on Friday. The Greyhounds defeated host San Diego State in game two on Wednesday night.