The visitor came flying out of the blocks and was two up after 15 minutes as it capitalised on some truly awful Magpies defending.
Jonny Evans escaped his marker to power home a header from a Robin van Persie corner and, from a Wayne Rooney delivery, Patrice Evra ghosted into the area to head home the second.
Newcastle put up more of a fight thereafter and Demba Ba was denied by the bar and then Papiss Cisse by a fine recovery save from David de Gea, the Spaniard clawing the ball away just before it could cross the line.
But Tom Cleverley sealed the points for the visitor with a cross-shot from the left which curled right into the top corner.
The win took the Red Devils level on points with Manchester City and four points behind leader Chelsea.
Goalkeeper Hugo Lloris was handed his league debut for Tottenham Hotspur but had very little to do as goals from Steven Caulker and Aaron Lennon gave his side a 2-0 win over Aston Villa.
Jermain Defoe's shot was heading wide when it deflected in off the heel of Caulker in the 58th minute and Lennon wrapped up Spurs' fourth straight league win with a low angled shot.
This latest success took Tottenham up to fifth, a point behind second.
Liverpool's disappointing season continued as it was held to a goalless draw by Stoke City at Anfield.
Jose Fonte scored two headers for Southampton, including a last-minute equaliser, as it drew 2-2 at home to Fulham.
Saints led after just four minutes, but an own goal from Jos Hooiveld made it 1-1 and Kieran Richardson looked to have won it for Fulham two minutes from time only for Fonte to salvage a point for his side.