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The Senegal striker's double blast took his tally to 10 league goals this season, putting him level with joint top scorers Robin van Persie of Manchester United, Luis Suarez of Liverpool and Swansea City's Michu.
Ba put Newcastle in front with a crisply-struck penalty into the bottom corner of the net after Wigan defender Maynor Figueroa was sent off for bringing down Papiss Cisse just inside the box in the 12th minute.
The home team made it 2-0 nine minutes later when Ba pounced on the rebound to score from close range after goalkeeper Ali Al Habsi could only parry a fierce 25-metre drive from full back Davide Santon.
Substitute Gael Bigirimana added a third goal, his first for the club, in the 71st minute when the Zimbabwean beat Al Habsi with a curling left-foot shot from 20 metres.
"It's been a difficult time for the players and staff because we've had so many injuries," Newcastle manager Alan Pardew told Sky Sports.
"It was nice to get an early break tonight. I'm not a lover of that rule," he said referring to the option referees have of sending a player off for stopping a goal-scoring opportunity, "but I did think it was a penalty".
Newcastle stayed 14th in the table with 17 points from 15 games, three points ahead of Wigan who are fifth from bottom.
"It became very difficult for us after 21 minutes, 2-0 down and only 10 men on the pitch," said Wigan manager Roberto Martinez.
"The sending-off was a big decision. For me the ball was between the two players and Figueroa should have been allowed to make a shoulder-to-shoulder challenge.
"To me the intention was to go for the ball. I thought it was too much of a punishment and it was harsh," added Spaniard Martinez.
At the other end of the table, Manchester United stretched their lead to three points with a 4-3 victory at Reading on Saturday and second-placed Manchester City were held to a 1-1 home draw by Everton.