The Tigers improved to 16-0 in the SEC opener while the Gamecocks dropped to 8-6.
Bonner led all scorers in the game with 29 points. She made 9-14 field goals and added six rebounds for the Tigers, who held a 36-26 rebounding edge.
Boddie hit 9-15 field goals and scored 21 points while adding four rebounds, three assists and two steals.
Auburn trailed 31-29 at halftime before taking the lead less than two minutes into the second period. Coach Nell Fortner's Tigers built their edge to 67-57 with 4:17 to play, but had to hold off a rally as the Gamecocks cut the margin to two points with 14 seconds left.
However, Alli Smalley, who scored 12 points, made two free throws with 12.7 seconds left and Bonner iced the victory with two more free throws with three seconds remaining.
Brianna Dickerson led South Carolina with 19 points as Auburn won its SEC opener for the first time since the 2001 season.
Auburn shot 52.6 percent from the field to 43.6 percent for the home team. Auburn was just 2-5 on threes while USC made 5-12. The Tigers made 18-24 free throws while South Carolina hit 23-26.
Auburn turned the ball over 21 times, two more than South Carolina. The Tigers blocked eight shots with Keke Carrier getting five of them. The six-foot-seven junior center led the Tigers on the boards with 10 rebounds and added six points. Sherell Hobbs scored eight for the Tigers.
Fortner said she liked the fact her team scored 51 points in the second half, but said the Tigers fouled too much and didn't play well enough on defense.
"I thought Whitney Boddie hit some big shots and DeWanna Bonner did," the coach said. "It was just, I guess, opening (SEC) game jitters and being on the road.
"This is the SEC," she added. "Every game has a lot attached to. It doesn't matter who you are playing, it doesn't matter what their record is. Every game is going to be like this. I am glad to get this one under our belt and move on to the second one."
Auburn returns to action on Sunday vs. 16th ranked Florida. Tipoff is set for 2 p.m. at Beard-Eaves Memorial Coliseum.