Ba signed off in style as United's hopes of retaining their Premier League title were dealt a fresh blow as they suffered back-to-back league defeats for the first time this season.
Free signing Ba plundered his 15th goal of the campaign in what seems certain to be his final appearance for the Magpies before heading off on African Nations Cup duty with Senegal.
Frenchman Cabaye sealed a first victory over Sir Alex Ferguson's men in more than 10 years with a stunning 47th-minute free-kick with Phil Jones' late own goal simply cementing their seventh place in the table.
Even Wayne Rooney's return from his exile could not spark United into life as Newcastle added to the pain inflicted on his side by lowly Blackburn at the weekend in front of a delighted crowd of 52,299.
Keeper Anders Lindegaard, who has repeatedly warned he had not joined United simply to "pick his nose", was handed a start in place of David de Gea, unlike Magpies midfielder Hatem Ben Arfa, who was named only among the substitutes despite declaring roughly the same sentiment in the run-up to the game.
Pardew sent out his side having seen them win just one of their last eight league games and knowing the challenge of improving on that run could hardly be much more difficult against a wounded United.
However, his players set about their task with a real relish and while they were forced to defend in determined fashion throughout, they did so more than competently with skipper Fabricio Coloccini and Mike Williamson in particularly miserly form.
In addition, they produced enough of an attacking threat not only to keep the champions on their toes, but to take a lead they rarely looked like relinquishing.
Indeed, Pardew's men, having survived an early scare when Coloccini just managed to cut out Ryan Giggs' attempted through-ball to Dimitar Berbatov in the opening minute, took the game to the visitors in the early stages.
Ba was uncharacteristically wasteful when he failed to make a meaningful connection with Danny Simpson's teasing fourth-minute cross, and Cabaye tested Lindegaard's mettle with a shot from distance two minutes later.
The Dane also had to deal with Cheick Tiote's skidding long-range drive, although as United worked their way into the game, it was they who started to threaten.
Tim Krul had to make a smart reaction save from Nani's 12th-minute snapshot, and the keeper managed to claim the rebound before the predatory Rooney was able to pounce.
Berbatov clipped the outside of the post with a deflected header three minutes later, but Newcastle were not content to sit back and defend.
They had been awarded and converted a contentious penalty in the 1-1 draw at Old Trafford in November, and they were appealing for another with 25 minutes gone, this time in vain, after Ba went down in a tangle of legs with Rio Ferdinand, the man whose challenge on Ben Arfa had been ruled illegal on home turf.
But the former West Ham frontman got his chance 12 minutes before the break, and as so often this season, took it in spectacular fashion.
Shola Ameobi climbed high above Phil Jones to flick on Krul's long free-kick and Ba swivelled instantly to smash a right-foot volley high past the stranded Lindegaard.
Ryan Taylor curled a 44th-minute free-kick just over after Tiote had left Rooney for dead with a neat trick and Ba prompted Giggs to foul him 30 yards out.
Lindegaard also had to deal with a nastily dipping Ba effort from distance in injury-time with the Magpies sensing an opportunity.
Jones' first season at Old Trafford has been largely exemplary, but the youngster's difficult evening on Tyneside took a further turn for the worse within seconds of the restart.
He barged Ba to the ground 30 yards out as the striker threatened to run away from him, and Cabaye curled the resulting free-kick in off the underside of the crossbar with Lindegaard once again helpless.
Central defender Williamson headed a 55th-minute Ryan Taylor corner just over with the Magpies pinning the visitors back to thwart their efforts to launch a recovery.
United would have been back in it within four minutes had it not been for old boy Danny Simpson, who somehow managed to block Rooney's point-blank volley from a Nani cross.
The visitors were enjoying their best spell of the game as Newcastle's defending became increasingly desperate.
But with no sign of a breakthrough, Rooney made way for midfielder Anderson with 15 minutes remaining, although United's efforts became increasingly toothless with the home side simply needing to maintain concentration.
That they did, and Jones' miserable evening was complete in the final minute of normal time when he headed Krul's deep free-kick into his own net.