Baines kept his nerve after Kevin Mirallas was pulled down by Maynor Figueroa in the box to claim a point for David Moyes' men, who had dominated much of the second half but until then failed to find a leveller.
Arouna Kone's 10th-minute opener for the home side was cancelled out almost instantly by a Nikica Jelavic header, but Franco Di Santo's 23rd minute strike put the attack-minded Latics back in control.
Both sides missed plenty of clear chances and Wigan almost won it in injury time when a shot from Shaun Maloney took an enormous deflection and looped over the helpless Tim Howard only to land on the roof of the net.
The livelier Latics deserved their lead when Maloney turned Seamus Coleman inside-out in the left side of the box before crossing for Kone to nod home the simplest of chances.
But it was a lead that lasted less than a minute, with Everton responding in almost identical fashion when Steven Pienaar floated a header from the left and Jelavic was unmarked in front of goal to head home from point-blank range.
Everton's best spell of the game came to an abrupt end in the 23rd minute when Kone dribbled in along the right touchline and beat Baines before pulling the ball back for Di Santo to ram into the roof of the net.
The recalled Di Santo almost grabbed his second and Wigan's third three minutes later with a fantastic 25-yard effort which Howard did well to tip round the post, then Maloney dragged a shot just wide as the Latics pressed forward in some style.
Leon Osman was unlucky not to equalise on the half-hour when his goal-bound shot inside the box took a big deflection off Gary Caldwell and was pushed over the bar by Ali Al Habsi, who also pushed a low Mirallas effort round the post.
And, as Everton ended the half strongly, they came even closer on 40 minutes when Baines dribbled a shot against the base of a Wigan post from a tight angle and the rebound bobbled in the six-yard box with no team-mate lurking to touch it in.
The first period ended in some controversy when Marouane Fellaini was booked for an aerial challenge on Figueroa which led to strong protests from the Latics who alleged the use of an elbow.
The visitors started the second half with more purpose, Mirallas making an early foray deep into the Wigan half, then the ever-dangerous Jelavic attempting a shot on the turn which flashed over Al Habsi's bar.
Baines cut the ball back for Mirallas to lash another effort just over in the 52nd minute, and the same player was threaded clean through two minutes later to try a low shot which Al Habsi brilliantly turned round the post.
But the Toffees were again reminded of Wigan's danger on the counter-attack in the 62nd minute when Di Santo set Maloney clear and the wideman's ball into the box was crucially intercepted by Phil Jagielka with Kone poised to tap it home.
Figueroa made a vital interception to deny Jelavic in the 76th minute as the striker swung back his leg to shoot, the Wigan man stretching to get an all-important touch despite strong Everton claims for a penalty.
When they spot-kick did arrive there were few complaints, Figueroa blatantly nudging Mirallas and giving Baines the opportunity to ram home the the equaliser to the relief of the massed ranks of Toffees fans behind the goal.
But Wigan almost grabbed the points back in the first minute of injury time when Kone played in Maloney, whose shot took a mighty deflection and looped over Howard only to drop agonisingly on the roof of the net.