The Cougars couldn't have asked for a better start, as Carlino hit a pair of 3-pointers and Brock Zylstra added another to give them a quick 11-3 lead.
Shots kept dropping for BYU over the next 10 minutes, and when Nate Austin made a layup, the Cougars had a 28-11 lead with 8 minutes, 55 seconds remaining in the half.
But Mercer found its stride after that, and the Bears crawled back into the game.
A couple 3-pointers by Langston Hall spurred the uprising, and Mercer trimmed the big deficit to four, 32-28, with just more than four minutes left in the half.
Five straight points by Davies righted the Cougars, however, and they took a nine-point lead into intermission.