It looked like they might when Craig Westcarr scored a minute before half-time, netting his fifth goal for the club.
But Blades boss Danny Wilson made two key substitutions at the start of the second half and one of the newcomers, Chris Porter, grabbed the equaliser just after the hour mark.
Walsall, really needing a win to boost their play-off hopes, dominated the first half but the visitors defended deep and enjoyed several close shaves.
Meanwhile, home defender Andy Taylor, playing against his old club, made one excellent tackle in the box to deny Jamie Murphy in the 23rd minute.
The Saddlers poured forward repeatedly and dangerman Febian Brandy missed a great chance, shooting wide after breaking clear in the 42nd minute.
But Walsall took the lead they deserved when Ben Purkiss combined with James Baxendale, who crossed low for Westcarr to beat George Long with a low shot.
Brandy missed a great chance to seal it for the Saddlers when he shot wide in the 51st minute with only the goalkeeper to beat.
Porter prodded the Blades level from close range after 64 minutes after Kevin McDonald's shot came back off a post.