The high court, in a decision handed down Friday, rejected Donald Younge Jr.'s claims that his prosecution occurred outside the statute of limitations.
He was convicted in 2009 on felony aggravated sexual assault and robbery charges in the Nov. 7, 1996 attack of a 23-year-old student as she walked from campus.
Prosecutors filed charges in 2000 against a "John Doe" to ensure they were within the four-year statute of limitations.
An FBI DNA database linked the victim and Younge in 2002, while he was being held in Illinois, and prosecutors re-filed the charges with his name.
Justices rejected his claim that the conviction should be overturned because a DNA match took too long, saying the state acted as quickly as possible under the circumstances.
Younge was sentenced in 2010 to spend up to life in prison for the attack of the university student.
He also was charged in the 1999 murder of another University of Utah student, but the charges were later dismissed.