This time, Stanford's offense showed some fight from the start.
Taylor, who finished with 142 yards rushing and two touchdowns, ran for 35 yards on seven carries before Nunes lofted an 11-yard touchdown pass to Ertz in the corner of the end zone to give the Cardinal a 7-0 lead on the game's first possession.
While the offense finally found its rhythm, Stanford's defense struggled to slow down Arizona's up-tempo style.
Ka'Deem Carey ran for 13 yards for the first of his three touchdowns, and John Bonano kicked a 34-yard field goal to give the Wildcats a 10-7 lead later in the second quarter.
Nunes stayed steady and sharp, finding Levine Toilolo for a 12-yard touchdown pass to put Stanford back ahead 14-10. Bonano kicked a 33-yard field goal to slice Stanford's lead to 14-13 at half.
The pace picked up even more following the break.
Scott threaded a 27-yard strike to Terrence Miller inches short of the goal line that set up Carey's short touchdown run to put Arizona in front 20-14 less than 2 minutes into the third quarter.
Although the Cardinal prefer to play grind-it-out games and control the clock, Arizona simply wouldn't let them.
The teams traded touchdowns for most of the second half until Jourdon Grandon stripped Ty Montgomery after a 16-yard catch early in the fourth quarter. Arizona recovered and took over at Stanford's 45.
Scott quickly led the offense down field and hooked up with Miller for a 10-yard completion that gave the Wildcats a 48-34 lead — the biggest either side had all afternoon. Scott nearly set the school passing record set by Willie Tuitama, who threw for a school-record 510 yards in a 48-41 win over Washington on Oct. 27, 2007.
Rodriguez opted to run the clock out with 45 seconds remaining from Arizona's own 19 with two timeouts and play for overtime, saying he "didn't want to make a mistake down there."
"Matt is a stud. He threw the ball well. We just needed to make one more play," Rodriguez said. "There's nothing to be ashamed of."
The Cardinal again showed its ability to bounce back after defeat.
Stanford has won after its last seven losses. The last time the Cardinal dropped consecutive games came in 2009, when it lost to Oregon State on Oct. 10 and Arizona on Oct. 17.
"It's huge," Thomas said. "To show that we can face adversity, overcome it and have that 16-round knockout fight really shows that this team's a high-character team that never gives up and has a never-quit mentality."
Antonio Gonzalez can be reached at: www.twitter.com/agonzalezAP