Wigan stormed back after Phil Jagielka's own goal early in the second half, but defeat cost the Latics an opportunity to continue their climb towards safety and survival in the big time.
Wigan newcomer Wilson Palacios, making his bow at the JJB Stadium, got off to an impressive, all-action start, operating wide on the left of midfield.
The Honduras international, snapped up on a three-and-a-half year deal after completing a loan spell at Birmingham City, fired a shot wide early on, and then set up a near post header for Emile Heskey who narrowly missed the target.
Wigan survived when Kevin Kilbane's clearance hit Bramble in the face, and fortunately went straight into Chris Kirkland's arms.
Everton then twice went close with Lee Carsley firing a free-kick over the bar, before Kirkland produced a point-blank save to deny the dangerous Mikel Arteta.
Tim Howard had to be alert to palm a powerful Marcus Bent header onto the bar when the former Everton striker had been left completely unmarked from Antonio Valencia's corner.
Everton lived dangerously again when Valencia seized the chance to shoot but this time Tim Cahill performed the rescue act blocking the shot.
Johnson had a sniff of a chance after Bent gave the ball away, but Bramble spotted the danger to deny him a clean strike at goal.
However, disaster struck Wigan when Bramble was punished for a mistake after he made a mess of his attempt to get the ball back to his keeper.
It allowed Johnson to nip in as the big defender lost his footing and the fleet-footed striker raced on to fire his shot into the net through Kirkland's legs.
Wigan had hardly recovered from that blow when Everton struck again with Lescott gratefully accepting the chance to bang in his seventh goal of the season.
The Latics grabbed a lifeline when Jason Koumas' free-kick bounced about in the Everton six-yard box, and eventually went into the net off Jagielka.
Wigan turned on the pressure in the hunt for an equaliser although Leon Osman missed a great chance to kill them off when he missed the target with a close-range volley.
The closest Wigan came to grabbing an equaliser came when Kilbane poked the ball wide from Koumas' free-kick and Bent fired over in stoppage time.