BYU (7-3) amassed 578 yards of total offense, including 421 yards on the ground, and held Idaho State (3-8, 1-6 Big Sky) to 287 yards of total offense.
Williams ran for 131 yards on 13 carries and tied a career-high with three rushing touchdowns. Hine went for a career-high 141 yards and one touchdown on just 10 rushes.
Taysom Hill went 11 for 19 for 153 yards and two touchdowns before being replaced just before halftime.
BYU received the opening kickoff and drove 60 yards over 12 plays to take an early 7-0 lead on a two-yard run by Williams. On the drive, the Cougars registered four first downs, and Hill opened the game hitting his first four passes and spreading the ball out to three different receivers.
Idaho State intercepted Hill on BYU’s next drive and used a series of run and pass plays to get the ball down to the 5-yard line. A pass interference penalty on third down gave the Bengals first-and-goal from the 2-yard line before having to settle for a field goal.
Williams increased the Cougar lead 14-3 on a career-long 70-yard touchdown the next time BYU had the ball. The long run came on fourth-and-1 and Williams took the ball up the middle and ran almost untouched into the end zone.
BYU forced Idaho State to punt for the third time in the first quarter and took over on offense from the Bengals' 49-yard line. Four plays later, Hill found senior Skyler Ridley for a 36-yard touchdown pass to increase the lead to 21-3 just 30 seconds into the second quarter. The touchdown grab was a career-long for Ridley.
The Cougars scored two touchdowns in 52 seconds to take a 35-3 lead with just over nine minutes left in the second quarter. Williams tied his career-high with his third rushing touchdown of the game, and Bronson Kaufusi returned an interception 12 yards for his first career interception and touchdown.
Hill found senior Richard Wilson alone in the back of the end zone for a 15-yard touchdown pass, and freshman Algernon Brown ran it in from 23 yards out to give BYU a 49-3 lead just before the end of the first half.
On the first play of the second half for BYU, Hine went off the right tackles and ran 64 yards to the end zone for his first career touchdown to put the Cougars up 56-3.
Senior Justin Sorensen added a 26-yard field goal in the third quarter, and Idaho State scored a touchdown and kicked a field goal for the final score of 59-13.
The Cougars return to action Nov. 23 at Notre Dame at 3:30 p.m. EST. The game will be broadcast live on NBC.