Constable netted inside six minutes at Kingsmeadow while substitute Smalley put the result beyond doubt with a late penalty as the U's extended their unbeaten away record and left the Dons now winless in six matches.
The visitors got off to a dream start when Asa Hall whipped in a fine cross from the right to pick out Constable, who fired a thumping header back across goal and into the net.
The Dons came close to an equaliser soon after but George Francomb just failed to make contact with George Porter's low cross.
The hosts started the second half brightly and had another chance after 55 minutes when Oxford goalkeeper Ryan Clarke had to block from both his own defender, Michael Raynes, and then Francomb.
But Oxford wrapped it up in the 82nd minute when Smalley was tripped in the penalty area by Rhys Weston and the substitute stepped up to seal all three points.