San Diego State, which trailed 21-19 at halftime, went ahead for good when Tim Shelton scored consecutive baskets and D.J. Gay hit a 3-pointer for a 26-21 lead less than two minutes into the second half.
The Aztecs have won all 10 games against its Division II opponents, winning the previous nine by an average margin of nearly 26 points. The outcome was the closest since 1969 when San Diego State won by five points.
UC San Diego missed its first eight shots to fall behind 9-0 in the first six minutes. But the Tritons went on a 21-4 run to take a 21-13 lead with less than four minutes left in the half.
The Aztecs made just one field goal in the final 10:57 to go into the half down by two.
Kelvin Kim scored 11 points to lead UC San Diego, which shot only 31.8 percent from the field.