It condemned high-flying Scunthorpe, chasing promotion to the Championship, to their first defeat in nine games.
In a lacklustre first half, Smith might have opened the scoring for Wrexham with a snapshot in the second minute which goalkeeper Joe Murphy saved.
Scunthorpe gradually began to take command without ever finding their top form.
Sixteen-goal marksman Billy Sharp was always closely watched by the Wrexham defence in which central defenders Shaun Pejic and Steve Evans were outstanding.
The best chance for the home side fell just before the interval when Andy Keogh lifted a shot over from close range following a right-wing cross from Cleveland Taylor.
But it was Wrexham who took command early in the second half. Midfield man Mark Jones took advantage of a poor clearance from goalkeeper Murphy to rifle back a shot from 25 yards that bulged into the back of the net past a despondent home keeper.
Scunthorpe pushed forward looking to try and get back on level terms, but could not get the better of a solid Welsh defence.
It was Wrexham who then made certain of victory when Smith forced the ball home from close range in the 65th minute to make it 2-0 from his side's only corner of the game.
Scunthorpe brought on substitutes Steve Torpey and Marcus Williams to try and repair the damage, but they made little impact.
Keogh did get the ball in the back of the net with a header after 82 minutes, but his joy soon turned to disappointment when he saw a linesman's offside flag.
It was a disappointing result for Scunthorpe who have had an excellent FA Cup record in recent seasons, reaching round three eight times in the previous nine years.
But this time they played second fiddle to a Wrexham side who grew steadily in confidence throughout the game and who now look forward to what they hope will be a big third round draw to boost the finances at the Racecourse Ground.
