It was the highest-scoring game for the Wildcats since a record 74-0 victory in 1921 over the Texas College of Mines and Metallurgy, the school that eventually became UTEP.
Tuitama completed 17-of-21 passes for 179 and three touchdowns to break the school record for career TD passes with 47, one more than Tom Tunnicliffe from 1980-83.
Grigsby carried 19 times for 169 yards, including two short touchdown runs as the Wildcats set a school record with 49 first-half points. That surpassed the mark of 42 set in 1976 against UTEP and matched against Pacific in 1980.
Arizona had a 521-112 advantage in yards in its first shutout since 1996.
The Wildcats, looking for their first winning season under coach Mike Stoops in his fifth year, rolled for 359 yards in a first half played in a steady rain.
The final first-half TD came on a 3-yard pass from Tuitama to Terrell Turner with nine seconds to play, the last of the 35 second-quarter points for Arizona.
The players were in kickoff formation when the decision was made to clear the field and advise the fans to leave the stadium as lightning flashed in the approaching storm. Most in the student section stayed.
The game began at 8:09 p.m. MDT, one hour and two minutes late.
Arizona went 80 yards in 11 plays on the first possession. Tuitama was 4-for-6 for 65 yards, and Grigsby scored on a 1-yard run.
Grigsby's 41-yard run set up the Wildcats' second score on a 5-yard pass from Tuitama to Mike Thomas that made it 14-0 with 1:15 left in the first quarter.
Thomas dropped an Idaho punt, but teammate Marquis Hundley picked up the ball and ran 87 yards for a touchdown that made it 21-0 with 13:17 left in the half.
The Vandals, 1-11 a year ago in their first season under Robb Akey, managed only one long-shot scoring try, a 54-yard field goal attempt by Tino Amancio that was wide right.
Idaho's Nathan Enderle was 10-for-25 for 48 yards with three interceptions. Deonte Jackson gained 25 in 10 carries.