The Broncos (6-0, 2-0 Western Athletic Conference) intercepted Hawaii's Inoke Funaki five times, turning three of them into 17 second-half points that put the game away.
The Broncos' smothering defense pressured Funaki all night, sacking him five times and holding the Warriors (3-4, 2-2) to just 288 total yards.
Moore finished 25-of-34 for 256 yards. The left-hander's three touchdown passes gave him 16 on the season and 11 over the last four games.
The victory was Boise State's 17th straight at home and avenged a bitter loss to the Warriors last year that cost them the WAC title. Hawaii, led by standout quarterback Colt Brennan, beat the Broncos 39-27 in the regular season finale in Honolulu, snapping Boise State's string of five consecutive conference titles.
Boise State had 367 total yards Friday, 111 on the ground by its corps of three tailbacks.
The Broncos took control in the third quarter when Thompson and safety Jeron Johnson intercepted Funaki on Hawaii's first two possessions, both times returning the ball into Boise State territory. The turnovers shifted momentum in a game that the Broncos led 10-7 at halftime and was statistically even.
On Hawaii's opening possession in the third quarter, Thompson stepped in front of an errant throw by Funaki and returned it to the Warriors 46-yard line. The Broncos scored six plays later when Moore tossed a 12-yard pass to Julian Hawkins to make it 17-7.
After the kickoff, Funaki, under pressure, overthrew his target and the pass was picked off by Johnson, who returned it to the Warriors 41.
Moore, a redshirt freshman, wasted little time making the Warriors pay when he capped a six-play drive by throwing a 16-yard pass to Austin Pettis that put Boise State ahead 24-7.
Early in the fourth quarter, Thompson again picked off Funaki at the Warriors 31. The Broncos' offense sputtered, but Kyle Brotzman kicked a 43-yard field goal.