A week after losing to No. 1 Oklahoma in their Big 12 opener, the Bears (3-3, 1-1 Big 12) never trailed Iowa State. Baylor's last conference victory had been 36-35 over Kansas on Oct. 22, 2006.
The Cyclones (2-4, 0-2) will have to wait three more weeks for another chance to break their 13-game road losing streak that dates back to the 2005 season.
Griffin, who was still playing high school football last October, has thrown nine touchdowns without an interception. He has rushing TDs in six consecutive games, the longest Baylor streak since Jerod Douglas' six in a row in 1995.
And Griffin can make a play while taking a hard lick.
On fourth-and-12 from the Iowa State 34 in the first quarter, with linebacker Jesse Smith charging toward him, Griffin released the pass just before being slammed hard to the ground. But Griffin's high-arching pass dropped into Wright's arms in the back of the end zone.
The officials used replay to confirm Baylor's first score, when Wright secured the ball while falling and landed with his knee just inbound.
Wright, who had seven catches for 132 yards, added a 51-yard score in the fourth quarter. He caught the pass in the right flat, came to a near stop along the sideline at the 40 and cut across the field. With Griffin among his blockers, Wright dived into the end zone near the left pylon.
Iowa State was coming off a 35-33 loss against No. 16 Kansas in which the Cyclones blew a 20-0 lead a week after an overtime loss at UNLV. Baylor led 38-3 before Austin Arnold's 9-yard TD pass to Bedrock Johnson with 9 minutes left.
Arnaud, the only experienced quarterback left after backup Phillip Bates quit the team this week, was 21-of-41 for 176 yards.
Jay Finley's 12-yard touchdown run and Griffin's 4-yard run capped consecutive long scoring drives for Baylor in the second quarter for a 21-3 lead.
In between those Baylor scores, Iowa State needed 17 plays to go 47 yards for Grant Mahoney's 34-yard field goal. And that doesn't even include six penalties for 40 yards in a span of 14 snaps after the Cyclones reached the Baylor 12.
There were false start penalties on consecutive plays before Mahoney kicked a 22-yard field goal. But when Baylor roughed the kicker, the Cyclones took the ball at the 2, only to be penalized three more times in five snaps before Mahoney kicked again.