The victory, coupled with Coventry's 1-1 draw at Millwall, leaves Gillingham trailing the Sky Blues on goal difference but the three points boost their hopes of edging clear of the bottom three.
The hosts got off to a flyer, taking the lead inside the first minute in comical fashion. Blackburn's on-loan left-back James McEveley's weak inswinging free-kick from the right should never have beaten the first man but somehow sneaked in.
Two Stoke defenders swung a leg aimlessly while falling over backwards only to miss embarrassingly. Steve Simonsen in the Stoke goal was caught unawares and looked stunned as the ball trickled apologetically past his despairing late dive and nestled in the bottom corner.
Two minutes later, the Gills should have doubled their lead as a ramshackle Stoke defence went absent without leave, allowing central midfielder Michael Flynn to scamper through the middle unopposed but with time, space and just Simonsen to beat, he scuffed his effort hopelessly wide.
Stoke were hanging on and breathed a collective sigh of relief that no Gillingham forward was following in Flynn's 19th minute free-kick as Simonsen spilled it back into the danger area.
Just before the half-hour mark, the Potters came within a whisker of equalising through captain Clive Clarke's venomous 30-yard free-kick but he was left holding his head in his hands when it cannoned away to safety off the corner of post and bar.
They were level ten minutes into the second half against the run of play as Kenwyne Jones headed in a floated free-kick from Gerry Taggart, taking advantage of a collision between goalkeeper Steve Banks and centre-back Chris Hope that left them both needing treatment for head injuries.
The last word went to Smith, though, who settled the match with a stunning right-foot volley from 20 yards in the 71st minute.