DeVille Smith scored with 3:30 to play to tie it at 50 but Tennessee-Martin never scored again, missing four free throws and three field goals.
Walden's jumper at 3:05 broke the tie then Eastern hit six of eight free throws for the win.
Timmy Knipp and Denzel Richardson added 14 points apiece and Eric Stutz had 13 for the Colonels (9-5). Eastern Kentucky was 4 of 23 from 3-point range but made 22 of 27 free throws. Richardson had 11 rebounds and four assists; Walden had five assists and made 8 of 11 field goals.