Christian Eriksen got in front of the dithering Antonio Valencia to nod in the winner in the second-half, after Emmanuel Adebayor had given Spurs a half-time lead.
Danny Welbeck swiftly halved the deficit, and although Hugo Lloris made a series of good saves late on, Spurs held off the threat of a United comeback to leapfrog them into sixth place.
Four of United's losses in the League this season have now come at home, with Spurs the latest conquerors after West Brom, Everton and Newcastle's triumphs.
The defeat will raise further question marks about the state of what many consider to be a flawed squad which is over-reliant on Robin van Persie and Wayne Rooney.
Rooney, back for the visit of Tottenham, did not look fully fit during the tea-time kick-off and Moyes even moved him back into midfield, again highlighting United's dearth of creativity in that particular area.
Tim Sherwood, however, has now taken 10 points from a possible 12 as Tottenham manager, with an FA Cup third-round tie at Arsenal to look forward to on Saturday.
They are now just two points outside of the Champions League places.