SAN JOSE, Calif. — When Shelvin Mack made a steal and quickly hit a 3-pointer in the opening minute of the second half, he had a good feeling Butler could shake its opening-game jitters.

By the time Mack sank his career-best seventh 3-pointer in the final seconds, he had made sure the Bulldogs were on their way in an NCAA tournament they hope will end with a hometown Final Four.

Mack scored 18 of his career high-tying 25 points after halftime Thursday, leading fifth-seeded Butler’s second-half surge in a 77-59 victory over UTEP in the first round of the West Regional.

Gordon Hayward added 13 points and Matt Howard 11 as the Bulldogs (29-4) won their 21st straight game to extend the sport’s longest active winning streak — but only after a dynamic rally from a six-point halftime deficit.

They were led by Mack, the sophomore guard who hit six 3-pointers on seven shots in the second half. Butler expertly spaced the floor and made patient passes with usual disciplined style, leaving even the talented Miners unable to keep up.

“It’s a great opportunity to do it on this stage,” Mack said. “You’ve got to knock it down like it’s open gym. ... My teammates did a good job giving me the ball. My job is to knock down shots when I’m open. That’s what I did.”

Butler advanced to face 13th-seeded Murray State, which surprised Vanderbilt 66-65 on a buzzer-beater by Danero Thomas.

Although the Final Four is still two weeks away, the players from this Indianapolis school already have considered how cool it would be to play in front of their hometown fans. The Shark Tank crowd, still hopping with energy from the Racers’ upset, also gave the small-school Bulldogs most of its cheers.

Derrick Caracter had 20 points and nine rebounds for UTEP, which won 16 straight games and a regular-season league title before a tournament loss to Houston last Saturday. The Miners (26-7) were a popular NCAA upset pick after the Conference USA power received a surprisingly low seed in the tournament.

“I’m not going to let these guys hang their heads,” UTEP coach Tony Barbee said. “I told them to be proud of the year they had. They’ve all gotten better. We had an outstanding year. Butler got hot at the right time, and we went cold at the wrong time.”

UTEP led 33-27 at halftime before the Bulldogs made a 22-4 run led by Mack, who hit five 3-pointers in the first 11 minutes while the defense harassed Caracter into ineffectiveness. Mack added his last 3-pointer with 32 seconds left, boosting the Bulldogs’ lead to a game-high 21 points.

“I think it’s deflating for any team when a team is suffocating you defensively and then going down and making almost every shot,” Howard said. “When you’re rolling like that, it has to get frustrating for the other team.”

Randy Culpepper added 16 points while absorbing two brutal hits in the second half, but the Miners’ defense couldn’t stop the patient outside shooting of the Bulldogs, who advanced in the NCAA tournament for the third time in four years.

“For us to lose in the first round is devastating, but every game is a lesson learned,” UTEP forward Jeremy Williams said. “They came out executing their plays, and we were sort of relaxed on defense. The second half, they just came out ready to play. We had them in the first half. We did everything we were supposed to do. They just came out a different team in the second half.”

Butler, which hit 10 of its 13 3-pointers after halftime, has the longest winning streak in Division I this season. The Bulldogs made a perfect run through the Horizon League, winning every conference game before also winning the tournament to capture a No. 5 seed in the NCAAs, matching the highest in school history.

UTEP was nearly as impressive during its run through Conference USA, with Caracter and league player of the year Culpepper largely dominating. But the Miners lost the tournament title game last Saturday, and Barbee acknowledged being mystified by their low seed.

While the Miners talked about respect, Butler went out and claimed it — just as these Bulldogs have been doing for decades.

Butler immediately took control after halftime, with Mack hitting two 3-pointers in the first 90 seconds. The Bulldogs took the lead on a 3-pointer by Willie Veasley, and after UTEP briefly went back ahead 37-36, Veasley’s free throw started Butler on its decisive 13-0 run.

“We were in the same position last year (in the NCAA tournament), down at halftime,” Bulldogs guard Ronald Nored said. “We didn’t make tough plays down the stretch. This year we actually came out and guarded in the second half and made tough plays down the stretch, which is different than last year.”

Butler didn’t repeat the mistakes of last year’s trip to the tournament, in which the Bulldogs fell behind 9-0 in a first-round loss to LSU, but UTEP still went ahead 17-10 midway through the first half. Butler, which has all five starters back from last season’s tournament team, reclaimed the lead with nine consecutive points, but the Miners went back ahead with strong inside play from Caracter.

The 275-pound Louisville transfer with a bushy mohawk scored 12 points — including a layup that dropped in just before the halftime buzzer. He had eight points after halftime, but just three rebounds.

“I was frustrated (because) I felt that we should have been winning,” Caracter said. “We weren’t executing as well as we could have defensively. (That) was mostly my fault, just me not coming out. I was just frustrated, because I know we were better than we showed today.”