Five Cougars reached double figures, led by Kyle Collinsworth's 19 points, and BYU improved to 4-2 in league play, 12-7 overall, in front of a sparse crowd of 2,137 at War Memorial Gymnasium.
"I really believe that our commitment to the defensive end of the floor won this game for us," Rose said.
In the game's key moments, the Cougars clamped down defensively on the Dons (4-3, 11-8) and wouldn't let go, something they didn't do when they opened WCC play with back-to-back losses at Loyola Marymount and Pepperdine.
Trailing 37-34 at halftime and getting "crushed" on the offensive glass, in Collinsworth's words, the Cougars started getting more loose balls, forced more one-shot possessions, and got what Rose called a "huge win for our guys, [making] Saturday's game [at Santa Clara] even more important."
San Francisco still shot 50 percent from 3-point range (5 of 10), but opportunities to launch one from long range were few and far between for coach Rex Walter's crew.
"Well, this is what I [have been] saying," Rose said. "I believe that we got away from how we win on the road [during four straight road losses in December]. We scored 112 points at Stanford, and we got to where we think we can just score and beat people."
With Collinsworth picking up a third foul early in the second half, and WCC leading scorer Tyler Haws having a quiet night for him 15 points on 5-of-10 shooting the unsung Cougars stepped up and delivered.
Matt Carlino scored 17 points off the bench, including 10 in the first half to provide a much-needed spark, and the player who replaced him in the starting lineup four games ago, Skyler Halford, was the catalyst in the second half.
Halford finished with 18 points after a slow start, and was 10-for-10 from the free-throw line in the second half to seal it.
"That 3-pointer [Halford] hit in the first half was huge because it got their guys to stretch out and let us put the ball on the floor a little bit," Rose said. "Obviously, Matt came in and gave us great minutes off the bench. And Eric [Mika], he fouled out, but he was physical and caused a lot of problems in there."
Mika took another hard fall and left the game for awhile, but returned and finished with 11 points before getting disqualified with three minutes, 29 seconds remaining.
Nate Austin didn't score, but grabbed eight rebounds. Still, the Cougars were outrebounded 40-29 overall, and the Dons scored 16 second-chance points, thanks to 16 offensive rebounds.
"We had a lot of really good play out of a lot of guys," Rose said.