Nacua's three interceptions ties Tyson Smith's school record set in 2000 against Wyoming.
The Cougars improved to 2-0, while the No. 20-ranked Broncos fell to 1-1 and lost for the second-straight time at LES.
Mangum struggled most of the night, but finished with 309 yards passing and two touchdowns with two interceptions.
Boise State's Ryan Finley threw for 297 yards, but three costly interceptions.
Jeremy McNichols' 3-yard touchdown on Boise State's first possession of the third quarter gave the Broncos a 17-7 lead.
Lethargic since a game-opening 84-yard touchdown pass from Mangum to Juergens, BYU's offense finally got moving midway through the third quarter when Mangum found Devon Blackmon wide open for a 70-yard gain.