Gonzaga (28-6) earned a 16th consecutive NCAA Tournament berth by shooting 52 percent from the field and limiting the Cougars to 36 percent shooting.
Gary Bell, Jr. netted 14 points and Kevin Pangos added 11 -- all from the foul line -- in the victory.
The loss means BYU's postseason fate will be determined by the NCAA Tournament selection committee on Sunday.
The Cougars (23-11), who were led by Tyler Haws' 24 points, went down big early and saw one of their stars, Kyle Collinsworth, exit with a knee injury early in the second half.
An incredibly slow start put BYU in a 25-9 hole 10 minutes in. During that span, the Cougars committed more turnovers (seven) than they made field goals (four), while the Bulldogs connected on 11 of their first 16 shots.
Drew Barham's second 3-pointer produced the 16-point lead, and it was a 21- point spread late in the half before consecutive buckets by Collinsworth made it a 44-27 difference at the break.
Collinsworth threw down an alley-oop dunk six minutes into the second half, but on the ensuing possession, the sophomore guard fell to the floor in pain after his right knee buckled.
After he was helped to the locker room after writhing in pain on the floor, his teammates responded with a 10-0 spurt to pull within 10.
Kyle Dranginis stopped the momentum when he beat the shot clock with a 3- pointer, and the margin did not dip into single digits until Frank Bartley IV hit one from long range to pull BYU within 63-54 with 4:08 remaining.
The Bulldogs failed to make a field goal over the final nine minutes, but they made crucial stops and Pangos made enough free throws down the stretch to close out the win.