The Magpies came into the game on the back of four consecutive Premier League defeats but this never looked like being a fifth from the moment Maynor Figueroa shoved over Papiss Cisse in the box.
Referee Mike Jones pointed to the spot and sent off the Latics defender before Ba converted the spot-kick to relax the mood at St James' Park after just 13 minutes.
The contest was effectively over just after the 20-minute mark when Davide Santon went on a driving run before firing off a long-range shot that Ali Al Habsi could only parry into Ba's path.
The Senegal forward, who is currently negotiating a new contract on Tyneside, nonchalantly tucked away the rebound for his 10th goal of the Premier League season.
Things could have got worse for the visitors before the interval when Gary Caldwell hauled down Ba having already been booked but he got away with a final warning and was promptly substituted at half-time.
After the break, Roberto Martinez's men produced a spirited performance and were perhaps the better side as they retained the ball well and probed in search of an unlikely comeback.
But a Newcastle break with 20 minutes remaining saw substitute Gael Bigirimana cut in onto his left foot and curl an effort into the far corner of the goal to put the result beyond any doubt.
The only sour note for Newcastle was that Santon and Ba both went off injured in the second half as the injury list at the club continues to grow.
But the three points were the all important thing and, although Newcastle remain 14th in the Premier League table, the victory lifts them five points clear of the relegation zone.
And the relief around St James' Park was in stark contrast to the concern etched on the face of Martinez as his Wigan team now host bottom club QPR in a relegation six-pointer on Saturday.