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.
"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".
"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.
