Just as improbably, that could save coach Rick Neuheisel, whose job security has been in question all season.
"Everything's great, right now," Prince said.
But the good might not have happened for him without all the bad.
Injured in the season opener, Prince missed his team's second game, against San Jose State, with a separated shoulder before returning at less than full strength to struggle in an ugly loss at Texas, a game in which he separated his other shoulder. His performance got him benched for the next two games, returning only when backup Richard Brehaut suffered a broken leg against Washington State a month ago.
"To get benched is something you don't want to ever deal with," Prince said. "But it definitely helped me to regroup mentally and physically, so that when I got back out there … and I got my chance to go back out, I felt good, I felt refreshed. It kind of gave me a chance to reflect and see what I could do better.
"So in a way," he said, "it was kind of a blessing in disguise."
The 5-4 Bruins have won three of their last four games with Prince back on the field, and have become so encouraged by their recent form that the quarterback refers to their humiliating 48-12 loss at Arizona as merely a "little setback" in Tucson.
At the time, though, many thought the lifeless display against a Wildcat team riding a 10-game losing streak against Division I teams and playing its first game after firing coach Mike Stoops would spell the end for Neuheisel.
"Nothing like a good dose of confidence," Neuheisel said.
That's partly how he explains the turnaround for Prince, who replaced Brehaut against WSU and led the Bruins to a come-from-behind victory.
The other part is health.
While on the bench, Prince was able to recover fully, and now he's effectively leading the team's option-based "pistol" offense, which relies heavily on the quarterback being able to run.
"That's always the thing that gives you headaches is when the QB can run the ball effectively," Utah coach Kyle Whittingham said.
That Prince can do.
Despite starting only five games, Prince is the team's third-leading rusher better on his feet than Brehaut, who returned to practice this week and one of three backs who average more than 5 yards per carry.
Running backs Johnathan Franklin and Derrick Coleman are averaging 127 rushing yards per game combined behind a huge offensive line, which is why Whittingham believes the Bruins have been better lately.
The Bruins average 233 rushing yards in their victories, but only 137.8 in their losses.
No team in the league runs more than they do, either 63 percent of time and Neuheisel acknowledged that makes for some anxious moments with a quarterback injured as often as Prince, who's facing the league's second-ranked run defense at Utah.
"But it's our way to play," Neuheisel said. The coach and Prince "had that conversation before the Cal game. We can't worry, we can't play nervous, we can't play scared. Let's go."
The Bruins can not only become bowl-eligible with their sixth victory if they beat the Utes but also take control of the race for the Pac-12 South Division title, something that seemed impossible at midseason.
But the Bruins came from behind last week, and took advantage of a series of Arizona State mistakes to beat the No. 19 Sun Devils 29-28 and move into a tie for the division lead with ASU and rival USC. The Trojans are ineligible for the inaugural league championship game, though, so the Bruins amazingly have several ways they could reach the title game on Dec. 3.
"We're just taking it one game at a time," Prince said. "We knew what was at stake with the Arizona State game, but we didn't want to look too far ahead to try to plan out things before they happened, because that's kind of what we did against Arizona and we got killed. So we didn't want to make the same mistake again."
"We're just keeping that Arizona game as a reminder that we don't ever want to feel that way again," he said.
at Houston L, 38-34
San Jose State W, 27-17
at Texas L, 49-20
at Oregon State W, 27-19
at Stanford L, 45-19
Washington State W, 28-25
at Arizona L, 48-12
Cal W, 31-14
Arizona State W, 29-28