Wilson fired the Red Devils ahead shortly before the hour mark - and it was enough to settle a game of few chances.
Headline team news saw Mousa Dembele return to action having missed our last two Premier League games, the Belgian international midfielder playing 90 minutes in front of a noisy crowd at the Lane.
Zeki Fryers and Nabil Bentaleb were also in the starting line-up, but it was Ruben Lameiras who was pulling strings in the middle at an early stage, turning inside Louis Rowley and threading the ball through for Souleymane Coulibaly in the fourth minute. While the latter had the ball in the net, a very early linesman's flag ruled out a breakthrough.
Josh Onomah tested goalkeeper Ben Amos with a low shot towards the near post, while Fryers rose highest at the other end to head away Andreas Pereira's free-kick.
Coulibaly dragged shots wide twice in as many minutes mid-way through the half after respective passes from Lameiras and Bentaleb, while Lameiras nearly set Onomah free behind the defence - only for Charni Ekangamene to intercept the ball with a well-timed covering tackle on the edge of his own area.
We had a flurry of chances around the half-hour mark but couldn't break down a stubborn United resistance.
First Kenny McEvoy tried a shot from eight yards out which took a deflection and hit the legs of wrong-footed keeper Amos, before the visiting stopper made a double save to deny Lameiras and then Coulibaly from a tight angle.
Lameiras sent McEvoy running free down the left channel shortly afterwards, but after taking an extra touch the nippy wide man could only find the side netting.
The second half began slowly, but it was given a spark on 58 minutes when substitute James Weir played the ball in to the feet of Wilson, whose shot on the turn crept beyond the diving Jordan Archer and low into the bottom corner of the net.
Three minutes later, Andreas Pereira chipped the ball delicately into the six yard box with the outside of his right boot, but Archer was there to gather.
The United defensive wall did its job on both occasions as we were subsequently awarded a pair of set pieces, with first Lameiras and then Connor Ogilvie seeing their free-kicks blocked by the line of bodies 10 yards away.
We might have levelled things up a minute before the end of normal time when Ogilvie battled his way to the left byline and pulled the ball back across goal, but it ran just behind Lameiras and the visitors were able to clear.
Lameiras had a shot blocked and was then off target from the rebound, while a low shot from substitute Daniel Akindayini didn't trouble Amos as United held onto their advantage until the end.
Spurs: Archer, A McQueen, Ogilvie, Bentaleb (Gallifuoco 67), Ball, Fryers (Lesniak 46), McEvoy, Dembele, Coulibaly (Akindayini 84), Onomah, Lameiras. Substitutes (not used): Dombaxe, Miles (GK).
United: Amos, Varela (Weir 19), James, McNair, Ekangamene, Pearson, Rothwell, Rowley (Harrop 78), Wilson, A Pereira, Janko. Substitutes (not used): Rudge, McConnell, J Pereira (GK).