Carlino also tallied seven rebounds, five steals and four assists. Senior Brock Zylstra chipped in a season-high 16 points and seven rebounds and sophomore Josh Sharp grabbed 10 rebounds to help the Cougars win their first conference road game this season.
BYU (12-4, 2-0) scored the first basket of the game before San Francisco (7-8, 0-2) hit three consecutive 3-pointers. Carlino converted a driving layup to end the run.
BYU regained the lead on a Zylstra trey that capped a 9-0 run to make it 11-9 with 15:47 left in the first half.
The Dons then went on an 11-2 run before Sharp ended the Cougar drought by hitting a short jumper to make the score 20-15.
With 5:57 left, Haws hit from downtown after a steal by BYU. Carlino also hit a three on the next Cougar possession, to cut the Don lead to 31-27.
Three minutes later, freshman Bronson Kafusi grabbed an offensive rebound and laid the ball to pull BYU within 10 at 39-29.
The next time down the floor, Zylstra made his second 3-pointer to bring BYU within nine at 41-32. He had the next five points for the Cougars, knocking down a shot from behind the arc with 1:10 remaining. Then he drove the lane and beat the buzzer with a jumper to end the half. The Cougars trailed 46-37 at the break.
Haws opened the second half with two quick baskets. Then after another San Francisco trey, Carlino stole an errant Don pass and dunked to bring BYU within six at 49-43, just two minutes into the half.
A double-teamed Davies hit a streaking Sharp for another BYU dunk on the next possession to cut the deficit to four at 49-45.
After San Francisco pushed the lead back to eight, Carlino hit a deep 3-pointer and Zylstra scored following a Sharp offensive rebound to bring BYU within five at 58-53.
San Francisco hit another three for a 61-53 lead but the Cougars responded with a 5-0 run to pull within three for the first time since early in the first half. Carlino and Haws both scored from the field during the run to cut the Dons’ lead to 61-58.
The teams then traded baskets and the Dons went back up by seven at 69-62 on back-to-back baskets by Cody Doolin and Tao Xu.
On BYU’s next possession Brandon Davies tallied an assist as he found Haws under the basket for a layup. The started an 8-0 run that included a Davies made a layup, a Zylstra fastbreak dunk and a Carlino fastbreak layup.
Carlino’s layup gave BYU its first lead at 70-69 since 11-9 at the 15:35 mark in the first half. The Dons retook the lead before Carlino stole the ball and scored on another layup to put BYU up 72-71 with four minutes left to play.
Haws made a long jumper with 2:46 to go to increase the Cougar lead to three at 74-71. The next time down the floor, Haws found a wide-open Craig Cusick for a triple to give the Cougars their largest lead of the game, 77-71 with less than two minutes remaining.
San Francisco made a free throw then a layup with 33 seconds remaining to bring the game within three, 77-74.
The Dons scored again on a BYU turnover, cutting the lead to one before Cusick got fouled with 12 seconds left. He made one free throw to put BYU up by two points.
In the final seconds San Francisco missed a layup, Carlino grabbed the rebound got fouled and made both free throws to secure the win, 80-76.