De'Jon Jackson tallied 13 points off the bench for San Diego (7-7), which got 10 points and 15 rebounds from Gyno Pomare.
Barry Stewart netted 17 points for Mississippi State (8-5), while Dee Bost contributed 13 points. As for Jarvis Varnado, he finished with 10 points, 13 rebounds and six blocks.
San Diego led 25-24 at intermission after limiting Mississippi State to 37.5 percent from the floor in the first half.
The Bulldogs were able to limit the Toreros to 31 percent shooting in the second half, and the score was deadlocked at 53-53 at intermission.
Mississippi State missed half of its eight free throws in overtime, while San Diego hit 5-of-6 shots from the floor in the extra frame.