Yohan Cabaye doubled Newcastle's lead with a 30-yard free-kick before Phil Jones diverted in a late own goal.
Wayne Rooney had a shot blocked on the line and Dimitar Berbatov's header hit the post for the champions.
Ferguson credits "fantastic goals"
The Jones howler, which came deep in stoppage time, summed up Manchester United's night at the Sports Direct Arena.
Visiting manager Sir Alex Ferguson said prior to the match that his side may be affected by the strong winds - and they indeed failed to cope in the difficult conditions as Alan Pardew's Newcastle thrived.
With Tottenham breathing down their necks, Ferguson will need to call upon all his great managerial experience to lift his players after two successive league defeats.
Alan HansenBBC Sport football expert
“Newcastle were sensational. They had every attribute for a team performance, but everything will worry Sir Alex Ferguson after this result. I expected a wounded animal after his team lost to Blackburn. ”
This was arguably his side's worst performance of the season, but the Magpies deserve credit because they were faster, stronger and sharper.
The home side won the key battles in the middle, while Manchester United centre-backs Rio Ferdinand and Phil Jones failed to cope with the muscle of strikers Ba and Shola Ameobi when the ball was pitched up.
At the other end of the field, Rooney and Berbatov were given little space by the Newcastle back four, with defensive midfielder Cheick Tiote producing another tireless performance as back-up.
Pardew hails 'good night' for Newcastle
The game may have turned out differently had Berbatov capitalised on Antonio Valencia's cross with the score goalless but his deflected header struck the base of Tim Krul's right-hand upright.
Manchester United's only other clear chance fell to Rooney, whose strike from four yards was blocked by Newcastle right-back Danny Simpson to preserve the home side's 2-0 lead.
Apart from those efforts, the Old Trafford side struggled to create. Nani occasionally delivered a dangerous ball, but the front two were often found dropping deep in order to bring themselves into the game.
DID YOU KNOW?
Man Utd have conceded three+ goals in consecutive league games for the first time since Feb 2004 (4-3 v Everton, 2-3 v M'boro).
This is the first time Man Utd have lost two Premier League matches by at least three goals in the same season since 2005/2006.
It is nearly seven years since Man Utd last lost two successive matches to teams from outside the Traditional Big Four, losing to Norwich City and Everton in April 2005.
For Newcastle manager Pardew, he will enjoy what is undoubtedly one of the best results of his managerial career.
His side took the lead in the first half when Ba picked up a flick from partner Ameobi and then hooked his shot past Anders Lindegaard, who conceded only his second goal in eight appearances.
Two minutes after the break, the Magpies extended the lead with one of the strikes of the season when France midfielder Cabaye curled in a 30-yard free-kick which bounced in off the underside of the bar.
The visitors' night came to a calamitous conclusion when keeper Krul's long punt downfield was misjudged by Jones, who diverted the ball into the net.
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