Webb's previous best was 27 points, against Arizona this season. The junior forward also had eight rebounds and four steals for the Broncos (8-4), who remained perfect at home this season.
''I felt good,'' Webb III said. ''The twos were falling, but the 3s weren't, and I can hit free throws now.''
Webb made 10 of 11 free throws and Boise State shot 28 of 34 from the line. It was the eighth time in 12 games that the Broncos attempted more foul shots than their opponent. Bradley shot 9 of 12 from the line.
''We tried to work inside out and get the twos to fall and the 3s would open up,'' Webb said.
''He scored 31 without hitting 3s,'' Boise State coach Leon Rice said. ''If he makes shots, he probably has 40 tonight. He's been working hard on all aspects of his game.''
Boise State made 6 of 20 from 3-point range and shot 45.9 percent from the field. Webb was 10 of 20 from the floor but just 1 of 6 from 3-point range.
Boise State trailed 3-1 early, but opened a 46-33 halftime lead by converting all seven of Bradley's first-half turnovers into 14 points. The Braves (2-10) finished with 14 turnovers, compared with six for Boise State.
''We were able to create offense from turnovers, and that's something we had not done a good job of that this year,'' Rice said. ''We got better at that today. We're starting to play well and improve.''
Mikey Thompson scored 12, Chandler Hutchison and Nick Duncan had 11 apiece and Lonnie Jackson 10 for Boise State, which led by double digits the entire second half. The Braves pulled within 52-42 with 16:44 to play, but Webb scored five points in a 13-2 run that put the game away.
''We're pretty unstoppable when we get more possessions than the other team because of the way we can score the ball,'' Hutchison said.
Dwayne Lautier-Ogunleye led Bradley with 17 points and Antoine Pittman added 15. The Braves hit a season-high nine 3-pointers and made only two fewer field goals than Boise State, but couldn't overcome the turnovers and differential in free throws.
Boise State seniors Anthony Drmic and Mikey Thompson both earned their undergraduate degrees and graduated Saturday. They join senior Lonnie Jackson, who graduated from Boston College last spring before transferring to Boise State, as player with degrees.
Bradley is the youngest team in Division I basketball with 10 freshmen on its roster and just three upperclassmen. The Braves haven't beaten a Division I opponent since winning their season-opener against Ball State.
WEST IS THE BEST
Sunday's game was a part of the Mountain West/Missouri Valley Challenge. Boise State's win was the sixth by the Mountain West, clinching the series. Fresno State and Evansville played later Sunday in the final game of the challenge.
INJURIES TAKE TOLL
Boise State had only eight players available for the game. Guard Montigo Alford and forwards David Wacker and Robin Jorch all were out with injuries.
Boise State hosts UC Davis on Dec. 30.
Bradley hosts TCU on Wednesday.