The Latics took a surprising lead when Paul Scharner ghosted in at the far post to head in Mario Melchiot's accurate cross on 57 minutes.
It did not take the host long to respond however when Louis Saha's header from Baines' corner found the back of the net.
David Moyes' side continued to press for a winner and their tactics paid off when substitute striker Jo won a penalty from Emmerson Boyce's clumsy challenge and Baines applied the finish to give Everton their first win of the season.
Defender Sylvain Distin made his Everton debut while another new signing, £10million Russian winger Diniyar Bilyaletdinov, was on the bench.
Everton made just one change from the side which lost their last league game at Burnley, with Marouane Fellaini dropped to the bench to allow Distin into the starting XI and Phil Neville reverting to a midfield role.
Wigan retained just four of the players who were knocked out of the Carling Cup by Blackpool in midweek - Michael Pollitt, Scharner, Boyce and Mohamed Diame.
With Everton likely to unveil more signings before Tuesday's deadline boss Moyes will soon have a new look about his team.
But they started the day bottom of the table and clearly needed a change of fortune.
Bright startEverton started brightly, with Tim Cahill seeing a diving header from a Baines corner go just wide, before Pollitt did well to turn over a fierce 12-yarder from Jack Rodwell.
Wigan's tackles were certainly flying in and eventually referee Lee Probert got his book out to caution Diame for a foul on Neville.
Wigan had created very little, although Charles N'Zogbia saw a shot from the edge of the area deflected wide.
But Everton almost scored with the best move of the half. Rodwell's turn and pass finding Leon Osman, who instantly sent Cahill racing away down the left.
The Australian's cross found Saha powering into the six-yard box, but Pollitt managed to get his body in the way of the striker's shot.
Skipper Mario Melchiot was the next Wigan man booked, for bringing down Steven Pienaar.
Even Moyes felt the strength of Wigan's tackling. As he bent down to collect the ball as it crossed the touchline in front of him, he was sent spinning by Hendry Thomas, who was sliding in trying to keep it in play. Both men finished in a heap on the track.
A minute later Boyce was cautioned for a foul on Saha, Wigan having just sent on Jason Scotland for the injured Diame.
Thomas was soon also in the book for breaking from the wall to charge down a Neville free-kick. By then Wigan had racked up 17 infringements to Everton's three in the opening period.
Within seconds of the restart, both Saha and Cahill failed to convert a Tony Hibbert cross as it flashed across the six-yard box, before Boyce made a brave saving tackle to stop Osman's 10-yard effort.
OpenerBut it was Wigan who broke the deadlock after 57 minutes. N'Zogbia crossed from the right and Scharner arrived unmarked at the far post to produce a diving header that Tim Howard could not keep out.
A minute later Osman was booked for a foul on Hugo Rodallega, by now Wigan were coming out of their shell.
And they almost had a second after 60 minutes when Jordi Gomez side-footed a Melchiot cross against a post.
However, Everton were level after 62 minutes, Saha emerging from a ruck of players to head home a Baines corner.
Everton then sent on Fellaini for Osman and in the melee of the first corner after the Belgian arrived, Joseph Yobo saw a towering header cleared off the line by Thomas.
Wigan sent on Won Hee Cho for Thomas, while Everton replaced Saha with Brazilian striker Jo.
Wigan replaced Rodallega with on-loan Chelsea winger Scott Sinclair with 10 minutes left, before Howard saved well from a Gomez free-kick.
N'Zogbia was booked for a foul and then Scharner became Wigan's sixth caution for bringing down Jo.
Everton sent on Bilyaletdinov with three minutes of normal time left for Pienaar, as they piled on the pressure.
Wigan broke out with Sinclair racing 70 yards to have his shot blocked by Howard.
But three minutes into injury-time, Boyce brought down Jo and Baines smashed home the penalty.
EvertonTeam StatisticsWigan Athletic2Goals101st Half Goals08Shots on Target310Shots off Target613Blocked Shots512Corners511Fouls243Offsides11Yellow Cards60Red Cards077.2Passing Success68.722Tackles2677.3Tackles Success65.455Possession4559.3Territorial Advantage40.7