A 65-percent free-throw shooter entering the game, Winder went 10 of 10 from the line.
"Ans was terrific tonight. That's a big lift for us, for all our guys," Rose said.
BYU improved to 11-5 in league play, 19-10 overall, and stayed in second place in the West Coast Conference with the win. The No. 25-ranked Zags fell to 13-2 and 23-5. It was BYU's first win over Gonzaga in the last six meetings.
"The feeling is unreal," Winder said.
Rose said he decided to start Winder instead of Skyler Halford for defensive reasons, mostly, and got the idea on the flight home Saturday from Moraga, Calif., after BYU beat Saint Mary's 60-57. He started Josh Sharp inside instead of Mika so Sharp would absorb the early fouls, instead of the mercurial freshman.
With Winder hounding Gonzaga sharpshooter Kevin Pangos during stretches and BYU's zone as good as it's been all season, in Rose's opinion, the Bulldogs were just 4 of 18 from the 3-point line. The Zags were 10 of 22 from beyond the arc in their 84-69 win last month in Spokane.
"The emphasis in practice was guard the 3-point line, whatever you do, guard the 3-point line," Winder said.
The Cougars did it despite an off night from Tyler Haws, the fourth-leading scorer in the country. Haws had just 12 points on 5 of 12 shooting. He reached double figures for the 42nd straight game, tied for sixth-longest in school history with Jimmer Fredette.
Still, he made the shot of the game, a running 3-pointer that beat the halftime buzzer and sent the teams into the locker rooms tied at 39. The momentum carried into the second half and the Cougars scored the first six points to go up by six.
Haws played only 13 minutes in the first half, due to having two fouls, but Rose put him back in with a few minutes left to give the Cougars a spark.
"He created a nice little shot at the end of the half and that gave us a big lift going into halftime," Rose said.
The Cougars never trailed in the second half, but couldn't pull away, either.
Matt Carlino's driving layup with 7:42 left gave BYU a 60-54 lead and got the crowd on its feet. He finished with 15 points and six assists in 31 minutes as starting point guard Kyle Collinsworth struggled, playing on a gimpy right knee.
The Cougars led by four or more the rest of the way.
Winder's free throws with 42 seconds remaining clinched it.
"I think it feels really good for our guys" to snap Gonzaga's winning streak against them, Rose said. " … Hopefully we can use this as a springboard."
Sam Dower Jr. had 10 points at halftime to lead the Zags, who were just 1 of 9 from 3-point range in the first half. He finished with a team-high 14 but was also saddled by foul problems and played just 20 minutes.
The Cougars made their first four shots and jumped to a 9-3 lead. But Gonzaga put together a 10-2 run to go up 13-11.
Halford triggered a 6-0 run to get the massive crowd into the game and when Mika made a pair of free throws, BYU was ahead 23-16.
The Zags missed their first six 3-point attempts, but when Gary Bell Jr. hit one with 8:03 remaining in the first half, BYU's lead was down to 28-21.
The Cougars led 34-24 with 5:30 left in the half, but the Zags rallied back with an 8-0 run.
The visitors took a 37-36 lead with 57 seconds remaining in the half on Ryan Edwards' 3-point play.
The Cougars were 4 of 7 from beyond the arc in the first half before missing all seven treys in the second half.
BYU 73, Gonzaga 65
Anson Winder goes 10 for 10 from the free-throw line and finishes with a game-high 17 points
Winder and Josh Sharp start for the Cougars as coach Dave Rose changes his starting lineup for the first time in 11 games
Eric Mika scores 13 points and grabs eight rebounds off the bench