The on-loan Newcastle forward headed the only goal of the game in the 16th minute as the Dons survived the 67th-minute dismissal of Daniel Powell to claim their third straight win.
The Milton Keynes club controlled the first half and skipper Dean Lewington had a bundled effort cleared off the goal-line by Kevin McDonald before Smith put them ahead. Dean Bowditch’s inswinging corner was headed towards goal by Lewington and Smith was on hand to nod in his first goal since 2007 from a yard out.
The Dons twice almost doubled their lead after the interval as Gary MacKenzie headed against a post from Lewington’s free-kick before Smith had a header cleared off the line by Michael Doyle.
The hosts were reduced to 10 men midway through the second half when Powell picked up his second booking in 14 minutes for hauling back Matthew Hill as he broke away.
The Blades piled forward late on but Chris Porter and Doyle placed their best chances too close to goalkeeper David Martin, while substitute Jabo Ibehre hit a post for the Dons at the death.