Dan Jech added 14 points and Eric Robertson 12 for the Coyotes (4-3), who took the lead for good on a 3-pointer by Casey Kasperbauer that made it 70-67 with 2:55 to play.
Venky Jois made two free throws to pull the Eagles (3-3) within 72-71 at the 1:38 mark, but McClelland answered with a layup and the Coyotes closed it by making 3 of 4 free throws while Eastern missed its last four shots.
South Dakota shot 71 percent in the second half (17 of 24) and finished at 58 percent for the game.
Bogdan Bliznyuk led Eastern Washington with 16 points and Cody Benzel made 4 of 7 behind the arc for 12. The Eagles were 9 of 17 on 3s in the first half but finished just 12 of 31.