Fischer made 6 of 9 field goals, including 5 of 8 from 3-point range, while Haws hit 9 of 16 from the field and all seven of his free-throw attempts.
The Cougars led by as many as 16 before taking a 47-36 lead into halftime.
Godwin Okonji hit a pair of free throws to pull Loyola Marymount (4-13, 0-5) within four, 53-49, with 13:51 remaining, but BYU responded with a 13-3 run and held on from there.
Marin Mornar led the Lions with 16 points.
Evan Payne, LMU's leading scorer at 20 points per game, did not play due to a violation of team rules.