Jackson, a starting cornerback and kick returner who also plays receiver for the football team, leaped 25 feet 8 inches to advance to the championship meet at Eugene, Ore., June 10-13.
La'Derrick Ward of Southern Illinois University Edwardsville finished first with a mark of 26 feet 8 1/2 inches. The top 12 finishers advanced to Eugene.
Jackson is one of 36 Trojans athletes competing in prelims at Texas.
Jackson won the Pac-12 championship on May 16 with a leap of 25 feet 3 inches at UCLA's Drake Stadium.