Neither team led by more than four points in a tightly contested second half. Following White's pivotal putback, he drew the fifth foul on Fresno State's Sylvester Seay and made two free throws to give the Aztecs a 58-56 lead.
Paul George tied the score for the Bulldogs with 45 seconds left by driving through four defenders for a layup.
Billy White then grabbed another offensive rebound on the other end, drew the foul and hit two free throws with 19.5 seconds left to put San Diego State ahead for good.
"At the end of the day, it's three or four offensive rebounds that really hurt us," Fresno State coach Steve Cleveland said.
Ladd had a chance to tie the game, but his runner bounced off the rim. Shelley grabbed the rebound and sank the clinching free throws.
Fresno State led 29-25 at halftime thanks in large part to Ladd's hot shooting. He scored 11 of the Bulldogs' first 16 points, including three 3-pointers.
The Bulldogs got off to a terrible start with two missed dunks and a 35-second clock violation. San Diego State led 8-0 before Fresno State called time out.