Grigsby carried 20 times for 135 yards despite sitting out the third quarter.
The shifty sophomore from Whittier, Calif., optimistically listed at 5-foot-10, had touchdown runs of 7, 27 and 14 yards to help the Wildcats take a 24-6 halftime lead.
He became the first Arizona back with three rushing scores in a game since Mike Bell did it against Washington in 2003.
Coming off a 70-0 rout of Idaho, the Wildcats have more than 100 points in their opening two games for the first time since 1954.
After punting on its first possession, Arizona scored on its remaining four possessions of the opening half.
Grigsby's 19-yard run started the Wildcats' first TD drive, and he ended it by going 7-yard for the score to make it 10-0 with 30 seconds left in the first quarter.
The Rockets, playing a Pac-10 team for the first time since 1991, didn't get a first down in the opening quarter but they moved the ball in the second, even though they couldn't get it in the end zone.
Alex Steigerwarld kicked field goals of 20 and 35 in the first half and 21 in the second.
Trailing 27-6, Toledo drove to the Arizona 1 in the third quarter but was pushed back a yard on each of the next three plays. Steigerwald's 21-yard field goal made it 27-9 with 3:17 left in the third quarter.
Tuitama's 9-yard touchdown pass to Delashaun Dean on the first play of the fourth quarter put the Wildcats up 34-9.
Toledo's touchdown came after Arizona's first turnover of the season. Terrell Turner caught a short pass and was hit by Beau Brudzinski. The ball popped loose and Damien McIntosh grabbed it in mid-air, returning it 9 yards to the Arizona 3.
Opelt threw to Williams on the sidelines for the score. Initially, it was ruled incomplete but was called a touchdown after a review, cutting the lead to 34-16. Arizona finished it off on a 12-yard TD pass from Tuitama to Thomas.
Steigerwald's three field goals make him 20-for-20 over the past two seasons, 23 of 24 in his career.