The Owls took a seventh-minute lead when Gary Teale’s cross was only cleared as far as midfielder Potter, who beat James Walker with a low 25-yard drive.
Walsall’s Liam Dickinson put a glancing header just beyond the far post while Reuben Reid saw his firm shot parried by Nicky Weaver.
Morrison headed narrowly wide and Tommy Spurr missed the target with a free-kick but, after Walsall substitute William Grigg tried a long-range effort that was parried by Weaver, the home side went 2-0 up.
Teale crossed from the left and Beevers found the net with a firm header 15 minutes from time as Wednesday wrapped up their fifth straight win in all competitions.
After Walsall’s Matthew Richards had a shot deflected wide, Morrison completed the scoring in the 83rd minute after meeting Teale’s cross with a near-post header.