Dann scored with his first touch after coming on in the 83rd minute after his team-mates had soaked up wave after wave of Pilgrims' pressure.
The giant defender, thrust into an attacking role for the League Two minnows as Saddlers' boss Richard Money sensed an upset, swept home a right-foot drive after being set up by fellow sub Mark Wright.
Argyle will rue not making the most of the large amounts of possession they enjoyed as Walsall set out to suffocate Argyle's attacking intentions. However, for all the possession enjoyed by the home side, they managed just two shots on target and rarely looked like achieving the penetration or width they badly needed.
The story could have been so different had Argyle striker Nick Chadwick not wasted a golden opportunity in the opening ten minutes.
Tony Capaldi and Sylvan Ebanks-Blake combined well to set up the former Everton man, who arrived at the far post unmarked only to blast the effort over the crossbar from inside the six-yard box.
Capaldi, too, had a good opportunity to break down the stubborn Saddlers, but his low drive when well placed just before the interval was well saved by Walsall goalkeeper Clayton Ince.
Other than that, the giant Trinidad and Tobago international had very little to do. The only other time he was tested was when Argyle substitute Akos Buzsaky fired off a long-range shot just before Dann's settler.
Not even five minutes of injury-time could save Argyle, who again finished a game strongly, but who must now pick themselves up for Saturday's visit to Stoke, managed by former Pilgrims' boss Tony Pulis.