The Hornets (6-4, 5-2 Mid-Eastern Athletic Conference), who have won five of their last six games, led 21-19 early in the fourth quarter.
Elko completed an 83-yard scoring pass to Tarpley to extend the lead, then Dae-Hon Cheung's 6-yard score made it 35-19 with 4:01 remaining.
On the ensuing kickoff, Antwon Chisholm scampered 59 yards, and Travis Champion threw his third TD pass of the day, a 30-yarder to Rashad Riddick, on the next play. After Hampton made the two-point conversion, Delaware State ran out the clock.
Tarpley, whose other TD was a 48-yarder, had five receptions for 171 yards and Nagee Jackson added scoring runs of 1 and 2 yards.
Jeremiah Schwartz rushed 136 yards for the Pirates (2-7, 2-5).
Linebacker Myles Jack, who suffered a season-ending knee injury, said Thursday he decided to leave UCLA and enter the 2016 NFL draft because he wants to be compensated for his skills.
The tougher tests await down the road for No. 3 Baylor Bears, but coach Art Briles has seen enough of his Bears to know this is his best team.
A decision has been made that Randy Edsall will not be the football coach at Maryland next season, and discussions are taking place about how and when to separate, a source said Thursday night.
Florida State running back Mario Pender has been released from the hospital but could be given a medical redshirt if he cannot return to the field this season.
Tennessee chancellor Jimmy G. Cheek has issued a statement amid rumors that alleges coach Butch Jones fought and punched senior offensive lineman Mack Crowder during a fall practice session.
The University of Wisconsin agreed to a 10-year deal with Under Armour on Friday worth a total of $96 million in cash and the retail value of products received.