The Magpies added to their list of high-profile scalps as they handed the new United boss his second defeat in four days, despite Robin van Persie making a long-awaited return.
The away team took the lead on the hour-mark, with Moussa Sissoko winning possession high up the pitch before pulling the ball back for Yohan Cabaye to roll the ball beyond the reach of David de Gea and into the bottom corner.
Robin van Persie, making his return from injury, looked the player most likely to salvage a result for United, and duly looped a header past Tim Krul moments after Cabaye's opener, but his celebrations were cut short by the offside flag.
The result sees Newcastle record its first win at Old Trafford since 1972, while, after losing to Everton 1-0 four days ago, United picked up back-to-back home defeats for the first time since 2002.
Moyes made one change in defense, bringing in Jonny Evans to replace Chris Smalling while making wholesale changes in his midfield.
Nani, Phil Jones, Tom Cleverley and Adnan Januzaj were all brought in following the midweek loss, with Van Persie returning from a groin injury up front in the absence of the suspended Wayne Rooney.
Pardew, meanwhile, made one change from his side's 3-0 reverse at Swansea City, bringing Anita into the midfield, with striker Shola Ameobi dropping to the bench.
Jones had the first effort of the game after eight minutes, forcing a comfortable save from Krul, before Cleverley had a shot inside the area that was well charged down by the visiting defense.
Loic Remy flashed a header wide for Newcastle, while Cabaye should have done better with an effort he pulled wide six minutes before the half-hour mark.
Pardew's side did well to stifle its opponent, limiting the defending champion to half-chances and, with Mathieu Debuchy seeing two efforts well saved late in the half, the scores were goalless at the break.
Krul was called into action in the second half, with Javier Hernandez getting a shot away after a lofted ball from Van Persie, before Patrice Evra's header was cleared off the line by a combination of Vernon Anita and the post. The former Ajax man will consider himself fortunate, though, with the clearance appearing to come off his arm.
Things then went from bad to worse for Moyes' men, as Sissoko burst down the flank and played an inviting low ball into the box for Cabaye, who stroked the ball into the net first time to hand Newcastle the lead.
Van Persie twice went close to canceling out that strike. His first effort saw him loop a header over Krul and into the back of the net, though he was flagged offside, before a swerving free kick almost evaded everyone to sneak in at the back post.
United applied pressure late on, though Krul was never overly troubled, and Newcastle held on to bounce back from the midweek defeat at Swansea in superb fashion and ramp up the pressure on Moyes.