Tyler Haws led the way with 31 points on 10 of 18 shooting and Carlino added 26 as BYU scored its most points since a 128-78 win over Sacramento State 20 years ago.
"I love it," Haws said.
It was the most points Stanford has given up since yielding 114 in a loss at UCLA in 1977, and the most points the Cardinal have given up at home since UCLA scored 120 on them in 1976.
The Cougars improved to 2-0, while Stanford dropped to 1-1 and its players walked away wondering what hit them. Dwight Powell had 28 points for the Cardinal, and Chasson Randle chipped in 33, a career high.
But it wasn't enough. The Cougars took their foot off the gas with about four minutes remaining, or it might have been worse.
"They did what they love, and they are good at it," Powell said.
Added Stanford coach Johnny Dawkins: "They are one of the fastest teams in transition that we've faced" in his tenure.
The output tied for the 16th-most points the Cougars have scored in a single game. They shot 53.5 percent from the field, and 8 of 15 from 3-point range, a marked improvement over last season. Poor free-throw shooting (28 of 43) was about the only bone Rose had to pick with his offense.
"I think, over the years, our program, we have had good wins on the road," Rose said. "But I don't know if they've been this early. We have got four or five pretty big games on our nonconference schedule. Hopefully, we can draw back on this win and realize this team could be really good."
Well, it can really score.
Freshman Eric Mika (12), Nate Austin (12), Kyle Collinsworth (14) and Anson Winder (10) also reached double-figures, and Collinsworth played a sensational floor game, Rose said, with nine assists and seven rebounds.
"I thought Kyle Collinsworth was so big in the first half" when BYU's other guys were in foul trouble, Rose said. "We played him all 20 minutes. He was the one guy who didn't have any fouls at half."
The Cougars took an eight-point halftime lead and extended it to 17 with 10:45 left in the game when Carlino scored eight straight points and Haws finished 9-0 run off with a jumper.
A Haws free throw gave BYU a 97-78 lead with five minutes left before the Cardinal put together a little run and made things mildly interesting. But Stanford could never get closer than eight points in the final minutes.
"It gives us a lot of confidence, coming into a place like this and getting a win," Haws said.
The Cougars played brilliantly on offense during stretches of the first half, building leads as big as 12 points before taking a 54-46 advantage at halftime.
They did it with Carlino mostly watching from the bench, as the guard scored seven points in the first five minutes of the game, then picked up his second foul. Collinsworth picked up the scoring slack with 12 points in the first half, and Winder added eight off the bench, including a couple of big 3-pointers.
No fewer than six Cougars had two fouls in the first half, but none had three.
Stanford shot just 41.7 percent in the first half, but stayed reasonably close by making 14 free throws. The Cougars shot 53.7 percent, but were just 5 of 11 from the line.
A poor 3-point shooting team last season, the Cougars were 5 of 9 from beyond the arc in the first half.
BYU went on a 9-0 run to take a 47-35 lead with Carlino and Haws on the bench, and almost stretched the lead to 15, but Winder missed an open 3-pointer. But a couple of impressive dunks by Powell righted Stanford, sandwiched around a 3-pointer by John Gage, who had 12 before fouling out.
Storylines: BYU piles it up
• BYU scores its most points since a 128-78 win over Sacramento State in 1993, walloping Stanford 112-103 on the road.
• Tyler Haws scores 31 points and Matt Carlino adds 26 as BYU shoots 53.5 percent and routs a Pac-12 team on its home floor.
• BYU shoots 8 of 15 from the 3-point line and leads by as many as 19 points in the second half.