The victory puts Gonzaga (35-2) in the Elite Eight for the second time, its first regional final since 1999. The Bulldogs will play Duke on Sunday.
UCLA (22-14) opened the second half with a 6-0 run to get within 35-34. Gonzaga scored the next 12 points, thanks to the powerful inside game of the 7-foot-1, 288-pound Karnowski to make it 47-34.
The Bruins, who lost in the Sweet 16 for the second straight year, were done in by a tough shooting night that included long stretches without scoring. They were led by Norman Powell's 16 points.
It was Gonzaga's second win over UCLA this season after beating the Bruins in December. Gonzaga's only loss to UCLA in the four-game history of the series came in a 73-71 defeat in the regional semifinal in 2006.
DUKE 63, UTAH 57
HOUSTON (AP) — Justise Winslow, the freshman from Houston playing at home the day after his 19th birthday, had 21 points and 10 rebounds for the top-seeded Blue Devils in their 63-57 Sweet 16 victory.
Duke (32-4) is going to its 20th regional final, the 14th under Mike Krzyzewski, the most by any active coach. Its last Final Four appearance was in 2010, when the Blue Devils also went through Houston on way to their fourth national title.
Freshman guard Tyus Jones had 15 points and Jahlil Okafor, the third freshman starter, had six points and eight rebounds.
Brandon Taylor had 15 points for the fifth-seeded Utes (26-9).
LOUISVILLE 75, NORTH CAROLINA ST. 65
Montrezl Harrell scored 24 points and reserve Anton Gill keyed a late-game surge for the Cardinals.
Louisville (27-8), the fourth seed in the East and seeking to make its third Final Four in four years, will play seventh-seeded Michigan State in the regional final on Sunday.
After toppling top-seeded Villanova, North Carolina State (22-14), the eighth seed, saw its post-season run end.
Terry Rozier had 17 points and 14 rebounds and freshman guard Quentin Snider added 14 points for the Cardinals.
Louisville coach Rick Pitino has a 12-1 record in Sweet 16 games, 6-1 with the Cardinals.
Trevor Lacey led the Wolfpack with 18 points, while Ralston Turner had 12 and Kyle Washington 11.
Anthony "Cat" Barber, the spark of the Wolfpack's attack, finished with eight points on 3-of-14 shooting.
MICHIGAN ST. 62, OKLAHOMA 58
Denzel Valentine scored 13 of his 18 points in the second half to lead Michigan State.
The seventh-seeded Spartans (26-11) are headed to the Elite Eight for the second straight year and fourth time since 2009.
Travis Trice led the Spartans with 24 points, while Branden Dawson had 11 rebounds.
Buddy Hield led the third-seeded Sooners (24-11) with 21 points.
Michigan State is the lowest-seeded team still in the tournament, and advances to face fourth-seeded Louisville on Sunday.
The game turned once Michigan State took its first lead, going up 44-42 on Dawson's 8-foot turnaround jumper with 9:26 left. The teams traded the lead four times before the Spartans went ahead for good with 6:42 left, when Matt Costello put back his own miss with an emphatic dunk.