Players said they fed off the intensity of the rivalry, even though the Cougars beat the Utes for the 10th time in the past 11 matchups.
The Utes did not capitalize on BYU's first-half woes, shooting 18 percent from the floor in the first half, and 24 percent overall.
At one point in the first half, the teams went more than six minutes without a field goal.
Watkins scored 14 points to lead the Utes in his first game since serving a one-game suspension for conduct detrimental to the team.
If one cluster of plays encapsulated the Utes' newfound commitment to effort, it came with 12:09 remaining in the second half.
The Utes trailed 36-24 when forward Javon Dawson saved a loose ball from out of bounds to Watkins, who laid it up.
The shot was goaltended by BYU's Noah Hartsock, but Farr, who had glued himself to the key since his initial miss, rose and plucked the ball from the air and dunked the ball through.
It was the kind of play good, scrappy teams make. Krystkowiak stomped his feet in approval. Yet, it was also the sort of sequence the Utes had not yet seen this season.
"It's really got to be a staple for us," Krystkowiak said. "We may be an underdog in every game we play this year from the Las Vegas bookies. There's no game on our schedule right now that we shouldn't come in and fight like dogs."