Clint Steindl added 12 points and seven rebounds for the Gaels (9-1), who have won seven straight.
Saint Mary's led by 17 late in the second half but had to hold on after the Eagles -- aided by a pair of technical fouls -- cut the gap to single digits. The Gaels made a season-high 32 free throws, 13 in the final 3:10.
Collin Chiverton had 18 points for Eastern Washington (6-6) before fouling out with 1:30 remaining. Cliff Ederaine added 11 points and eight rebounds while Jeffrey Forbes had 10 points for the Eagles, who have lost four of six.