The 27-year-old's first-half double ended a run of four successive league defeats for the injury-hit Magpies on a day when it emerged that the club's ongoing efforts to renegotiate his contract to dispense with a troublesome release-clause are yet to pay dividends.
But Alan Pardew's men were aided in no small part by the controversial 12th-minute dismissal of Honduras international Maynor Figueroa by referee Mike Jones, who later opted not to send off Gary Caldwell for what looked like a second bookable offence.
Ba, who worryingly for his manager limped off late in the game, converted the resulting penalty and then took his tally for the season to 10 with a close-range finish after Davide Santon's shot had been parried, with substitute Gael Bigirimana's superb first goal for the club cementing just a second league victory in 10 attempts.
Newcastle, unlike last season, have endured more than their fair share of bad luck to date during the current campaign with injuries and suspensions having robbed Pardew of key players just when he needed them most.
But fortune favoured them spectacularly in their hour of need on Monday evening as they attempted to avoid the ignominy of a fifth successive defeat for the first time in the Premier League.
There were 12 minutes on the clock when Vurnon Anita picked out Ba and he slid the ball into the run of strike partner Papiss Cisse.
Figueroa came across to challenge the Senegal international, who ended up in a heap on the ground with Mr Jones interpreting his intervention as a penalty offence.
Having made that decision, he then had little option but to dismiss the defender and with the Wigan bench still furiously arguing their case - and wing-back Jean Beausejour having been booked for his protests - Ba thumped the spot-kick low to keeper Ali Al Habsi's right to open the scoring.
Until that point, the visitors had more than made a fist of a game in which they knew they would encounter a side short on confidence, with Tim Krul having to dive full length to turn away Franco Di Santo's well-struck fourth-minute effort.
But Figueroa's premature departure changed the shape of the contest and after Ba and Jonas Gutierrez had both gone for goal from distance, manager Roberto Martinez decided to shore up his team by preparing to withdraw the attack-minded Jordi Gomez and send on James McArthur in his place.
However, before he could make the change, the Magpies increased their lead.
Left-back Santon headed forward in determined fashion with 21 minutes gone before cutting inside and unleashing a right-foot piledriver which Al Habsi simply could not handle, and Ba was in the right place at the right time to tap home the rebound.
Any anxiety which the home side had felt - and even experienced campaigners Fabricio Coloccini and Cheick Tiote had fallen victim at times - evaporated as they started to stroke the ball around and make the most of their numerical advantage.
The game might have been effectively over nine minutes before the break when Wigan skipper Caldwell, who had earlier been cautioned for a crude tackle from behind on Ba, felled the same man on the edge of the penalty area but Mr Jones was generous in the extreme as he awarded only a free-kick.
Frenchman Sylvain Marveaux, who had been handed a free role behind Ba with Cisse starting wide on the right, curled the resulting free-kick inches over the angle of post and crossbar.
Wigan regained a measure of composure as the half-time whistle approached, but they headed for the dressing room knowing the odds were heavily stacked against them.
Caldwell was conspicuous by his absence as the sides returned for the second half with Adrian Lopez having taken his place, while Tiote, who had picked up a knock before the break, was replaced by Bigirimana.
Pardew was forced to make a second change within four minutes of the restart when Santon limped off to become the latest man to join a worrying casualty list and was replaced by Shane Ferguson.
To their credit, Wigan took the game to their hosts in the early stages of the half, but it was Al Habsi who had to get down well to keep out Marveaux's 52nd-minute strike after he had turned smartly on to Anita's pass and carved his way into the box.
The Frenchman, enjoying perhaps his best night yet in a black and white shirt, turned provider four minutes later to set up Bigirimana, whose side-footed effort was saved by Al Habsi, and Cisse sent a dipping 59th-minute effort over the bar.
However, the former Coventry midfielder was not to be denied and when Marveaux found him wide on the right with 19 minutes remaining, he cut inside to curl a fine left-foot shot past the keeper and inside the far post.