Johnson, who led the nation in scoring last season with 25 touchdowns, was injured last week against Nevada and did not travel to Ruston. Without him, Boise had 465 yards total offense.
The Broncos (6-1, 3-0) have lost only one Western Athletic Conference game since 2002.
The game went back and forth for 3 1/2 quarters, but a Tech fumble and Tharp's two touchdown passes in the fourth quarter ended any chance of an upset.
Tharp was 21-of-35 for 328 yards with two interceptions.
As the Bulldogs (2-5, 1-3) were putting together a drive that might have tied the game in the fourth quarter, Orlando Scandrick stripped the ball from Joe Anderson on the Boise State 13.
Two plays later, Tharp connected with Jeremy Childs for an 83-yard touchdown to make it 38-24 with 6:38 left in the game.
Coming into the game, Tech's longest play from scrimmage was a 34-yard run by Patrick Jackson, but the Bulldogs made a few big plays that helped keep the game close.
The first was a 46-yard touchdown run by Jackson that tied the game at 7. Daniel Porter ran 74 yards for a touchdown -- the eighth-longest in school history -- to tie the score at 24.