Visiting United were second best for large parts of the opening 45 minutes as Spurs enjoyed large spells in possession.
The home side fought they had broken the deadlock in the 34th minute when Emmanuel Adebayor flicked the ball into an unguarded net from close range. However, the Togo striker was penalised by referee Martin Atkinson for controlling the ball with his hand prior to converting his chance.
Just as the two teams looked to be heading into the break level, United opened the scoring with virtually their first effort on target. Wayne Rooney evaded his marker Kyle Walker to nod a corner from Ashley Young past Brad Friedel in the home goal.
Benoit Assou-Ekotto then grazed the crossbar with a curling effort from 25 yards out, but it was United who grabbed the second goal of the encounter.
Walker failed to clear Nani's cross from the byline and Young was on hand to send a half-volley past a wrong footed Friedel on the hour mark.
The England international added his second and United's third nine minutes later, curling an effort into the top corner of the net from 20 yards out.
Substitute Jermain Defoe pulled one back for Spurs three minutes from time when he collected a poor pass from Ryan Giggs and shot past an unsighted De Gea from the edge of the area.
However, Defoe's late intervention failed to produce a late comeback as United held out for all three points.