Mossley levelled after Chase keeper Curtis Pond conceded a spot kick and Max Leonard fired home from 12 yards.
Mossley took the lead just before half time as Ben Halfacre had a shot deflected past Pond.
The hosts confirmed the points midway through the half. Chasetown gave the ball away and Mike Fish ran through and netted.
Mossley came close to a fourth but Pond repelled several attacks.