Matthew Richards bagged a stunning free-kick to put Walsall on their way to a comfortable 2-0 victory and leave Stockport in even deeper relegation trouble.
The Saddlers midfielder struck in the 37th minute when he rifled a left-footed shot into the top corner from 30 yards out.
Stockport - who have now lost four League One matches in succession - went close through Nicholas Bignall and Paul Turnbull.
Deeney also struck a post with a fine left-foot strike from 18 yards, before striker Darren Byfield added a killer second in the 56th minute when he converted Deeney's low cross.
The result allowed the Saddlers to record a third successive home win as sorry Stockport were left contemplating the dismal prospect of a relegation dogfight.
Stockport may have had a penalty when home keeper Clayton Ince went down at the feet of Peter Thompson, then Ince pulled off a tremendous save to deny substitute Oli Johnson 10 minutes from time.
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