Ba scored twice before the break to put 10-man Wigan on the back foot, before Gael Bigirimana curled home the third with in the 71st minute.
Newcastle's efforts to negotiate a new deal with the player, which would remove an escape clause in his current contract that reactivates in January, have so far come to nothing.
"The truth of it is that Demba has got a clause in his contract and it is still hanging over us," Pardew admitted after the match
"We have tried to negotiate away and we have not managed to do that as yet.
"But the one thing I will say on a positive note is that he has never, if I am honest, looked me in the eye and looked like he wanted to do anything else but stay here, and I hope he does."
Newcastle enjoyed a significant slice of good fortune with 12 minutes gone when referee Mike Jones ruled a Maynor Figueroa's challenge on Papiss Cisse was not only worthy of a penalty, but also a red card.
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 wingback 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.
Less than ten minutes later, Newcastle left-back Davide Santon headed forward in determined fashion 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.
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.
The visitors responded well to make a real fist of it after the break, but Pardew's side remained a threat on the counter and when the impressive Sylvain Marveaux picked out substitute Bigirimana with 19 minutes remaining, he cut inside to curl his left-foot shot home and claim his first goal for the club.
Pardew was a relieved man as he savoured a win which could not have come at a better time.
He said: "It was a massive victory for us, and I am very proud of my staff and my players because we have had to stand tall.
"Four defeats in this city isn't easy for any team, I don't think. There was a lot of pressure on us."
Roberto Martinez, the Wigan coach, was bemused by the sending-off - a decision which he believed proved key.
The Spaniard, who revealed the club will consider an appeal, said: "You need to understand, Maynor is as honest as you are going to get. He is one of the most honest footballers I have ever worked with.
"When he makes a rash challenge, or if he makes a challenge he feels is clearly breaking the law, he will accept responsibility.
"He was destroyed. He was very, very upset at half-time. All he was saying was, 'I challenged, I went shoulder-to-shoulder and the ball was there to be won'.
"If you look at the replay, that's exactly what it was, so I do feel for my player. He didn't do much wrong.
"It's a decision that really changes the dynamics of the game, but then to concede from a penalty is clearly a double punishment."
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