The Senegalese forward struck twice after Maynor Figueroa's early red card, with Gael Bigirimana's second-half effort putting to bed the Magpies' four-game losing streak
The Senegal international was on target twice in the opening 45 minutes, with Gael Bigirimana's superb curled effort capping off on a confident return to form for Alan Pardew's men.
For the hosts, Pardew made one change to the side that fell to a late 2-1 defeat against Stoke on Wednesday, with Sylvain Marveaux replacing the suspended James Perch in midfield. Fit-again Shola Ameobi was available from the bench.
Gary Caldwell returned to the centre of defence for Wigan, with Adrian Lopez making way for the club captain, while Franco Di Santo and Arouna Kone continued in attack.
Keen to quickly calm any jittering nerves after their woeful form of late, Newcastle could not have hoped for a better start. Senegalese striking duo Ba and Papiss Cisse linked up to play the latter through in the box, only for Maynor Figueroa to barged into the Newcastle No.9 as he looked to pull the trigger.
The Wigan man paid the price with a red card, and Ba duly dispatched from the penalty spot to put his side a goal to the good.
Eight minutes later, the former West Ham man was on hand again to double the lead. Ali Al-Habsi did well to thwart Davide Santon's vicious drive from distance, but the shot-stopper had no chance against Ba from the rebound, who tapped home his 10th of the season.
The visitors were lucky to end the half with 10 men after Caldwell hauled down Ba on the edge of the box. Already on a yellow card for a mistimed challenged on the striker earlier in the game, the Scotsman was given the benefit of the doubt by referee Mike Jones.
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That would be the Italian's last act of the evening, as he was forced from the field with a groin injury to be replaced by Shane Ferguson.
Dutch right-back Stam continued to provide Wigan's attacking threat, while Marveaux, who endured a quiet first half, burst into life for the hosts with a series of silky runs to open the away side's back line.
However, it was Bigirimana, introduced at half-time for Chiekh Tiote, who would make the first real impact of the half. The 19-year-old received the ball on the edge of the area, before curling a left-footed effort past Al-Habsi to score his first goal in the Premier League.
The cold evening did not come without it's sting for Pardew, however, with Ba a late casualty to injury, meaning he could be a doubt for the visit to Fulham next Monday - another key clash if Newcastle are to put the rot behind them once and for all.