Clinkscales finished with 15 points, including four 3-pointers, and Walker added 14 as the pair made up the bulk of the Mustangs' 36 points from the bench.
Southern Methodist (4-3) shot a little better than 45 percent from the field. They took the lead about seven minutes into the game and never gave it back. Starter Justin Haynes finished with 13 points.
The Tigers (5-4) shot just 35 percent from the field and about 19 percent from long distance.
But Occidental's Sean Anderson led the game in scoring with 16 points, shooting 7-for-10 from the field.