Ba could only look on in horror as John O'Shea's 85th-minute header hit him and sailed past helpless keeper Tim Krul.
The Black Cats could scarcely argue it was deserved after failing to make the most of Cheick Tiote's 25th-minute dismissal for a studs-up challenge on Steven Fletcher.
Yohan Cabaye had got the Magpies off to the perfect start with just three minutes gone and the visitors held on to their lead relatively comfortably until a final onslaught.
Sunderland, despite seeing plenty of the ball, were rarely able to trouble Krul as Adam Johnson, James McClean and Stephane Sessegnon struggled to provide any meaningful service for frontman Steven Fletcher.
But although they emerged with a point, the Black Cats have won only one home league derby since 1980, and have now tasted victory home or away against their neighbours on just one occasion in the last 16.
Newcastle left perhaps feeling they should have been doing so with all the points after staging a brave rearguard action in which returning skipper Fabricio Coloccini was superb, but satisfied to have come away with something to show for their efforts after Tiote's premature departure.
It took less than three minutes for an eagerly-anticipated encounter to catch fire, although it did so in painful style for the home fans.
Hatem Ben Arfa found space down the right and played the ball in to Ba, whose shot from a tight angle was blocked by keeper Simon Mignolet at his near post.
However, the Belgium international could only turn the ball into the path of the fast-arriving Cabaye at the edge of the box and his low drive was true and powerful and flew into the back of the net to send the travelling fans behind the goal into delirious celebrations.
Sunderland's response was immediate and Mike Williamson had to intervene to prevent Fletcher from reaching Sebastian Larsson's teasing right-wing cross four minutes later.
But for all the Black Cats were enjoying the greater share of possession, they lacked penetration and Krul had to field Larsson's 17th-minute free-kick, but little else.
O'Shea made an important block to keep out Ba's volley seconds later as Newcastle continued to pose the greater threat.
However, the game changed with 25 minutes gone when Newcastle's midfield enforcer Tiote was sent back to the dressing room after careering into Fletcher.
Referee Martin Atkinson had already blown for a foul on the Ivorian by Jack Colback, but his momentum carried him into the Scotland international and as the home fans bayed for blood, the official produced a red card, much to Tiote's astonishment.
The visitors temporarily re-organised by dropping striker Ba into a deeper role, but manager Alan Pardew eventually introduced James Perch in an attempt to plug the gap with derby specialist Shola Ameobi reluctantly making way.
In the meantime, Johnson had curled a left-foot effort high and wide, and full-back Craig Gardner had smashed a 35th-minute free-kick inches wide and seen another effort blocked by Williamson's backside.
But the Magpies might have increased their lead four minutes before the break when Coloccini's shot from a well-worked corner was blocked and Ba acrobatically hooked the ball over the bar after controlling the rebound.
Sunderland returned in determined mood and went close within two minutes of the restart when Fletcher headed across goal from another Larsson cross.
But Newcastle were refusing to sit back and Mignolet had to pluck a deflected Ba shot out of the air after Cabaye had found him 25 yards out.
The home side were once again dominating possession, but a succession of poor final balls let the visitors off the hook with the locals growing increasingly restless.
Newcastle were defending deep and trying to hit their hosts on the break, although as the clock ticked towards the hour-mark, the traffic was largely one-way.
Coloccini deflected McClean's 64th-minute shot wide seconds before Martin O'Neill withdrew the ineffectual Sessegnon to send on former Magpies striker Louis Saha with the temperature rising inside the stadium.
The pressure was mounting all the time, but with Coloccini and Williamson in commanding form at the back, Krul continued to enjoy enviable protection.
Newcastle could have increased their lead nine minutes from time when Cabaye and Ben Arfa staged a lightning break before the latter fed Ba, whose shot was blocked by O'Shea.
Saha might have levelled seconds later, but fired into the side-netting from McClean's flick-on, but redemption was close at hand.
O'Shea met Larsson's deep free-kick with a header which hit Ba and flew past Krul into the net to allow the home fans to breathe again.
McClean and Gardner both went close in a late flurry, but Newcastle saw out time to return to Tyneside the happier of the two sides, but wondering what might have been.
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