A late salvo from Wigan Athletic looked on when Arouna Kone prodded home to drag the score to 2-1 but, the earlier goals from Leon Osman's deflected effort and a Phil Jagielka header proved too much of a mountain to climb.
There were late half chances as Latics looked to flood the box with players but, spirits were eventually dampened when the referee blew for full time after four added minutes.
Roberto Martinez had the luxury of bringing back Gary Caldwell into the starting line-up for the first time since Newcastle United away as he replaced Franco Di Santo in a tactical re-shuffle.
Latics looked to crowd out Everton's creative midfield as James McCarthy, James McArthur and David Jones played in the centre but, Everton found gaps at crucial times.
It was a case of good in two thirds for both sides in the first half as Everton created chances but couldn't finish and Latics provided excellent build-up play but, couldn't find the final pass.
The first half went by with rare incident as both sides had tame efforts saved and seen wide.
Ronnie Stam and Shaun Maloney provided the best of the efforts for Latics, with Maloney curling a free kick towards the top corner for Tim Howard to save and Stam striking left footed from range which was gobbled up by the keeper.
Everton came out the brighter at the start of the second half and it looked ominous that a goal would come as players started to get between Latics' defensive and midfield lines.
Eventually the hosts got that hint of fortune needed to take the lead in such a tight game and when Osman wasn't closed down on the edge of the area, his right footed effort cannoned off the hand of Caldwell to fool Ali Al Habsi and nestle into the back of the net on 52 minutes.
Six minutes later and Latics were outraged after the goal scorer seemingly brought down Shaun Maloney in the box.
Maloney's movement on the ball looked to have fooled Osman after he cut in from the left wing but, Lee Mason said no penalty despite contact between the two players' knees, with Jean Beausejour receiving a yellow card after and overzealous reaction.
Latics had their tails up for a spell as their sense of injustice spurred them on.
The move of the game almost provided a quick payback when David Jones's pass down the right of the box found Maloney who cut the ball into the danger zone along the ground for Kone to finish but, in came Phil Neville to slide in and block what looked destined to be a goal.
Just as Latics looked to be reaching that equalising goal, Everton doubled their lead as a short corner from subsitute Bryan Oviedo was clipped into the box by Neville and headed home by Phil Jagielka who out-jumped Caldwell to the ball.
There was a sense of three points coming from the Everton crowd but on 82 minutes Kone gave them something to be worried about when he poked home from close range.
Franco Di Santo's excellent close control on the edge of the area resulted in a blocked left footed shot which started to spin in the air as it dropped between Jagielka and Sylvain Distin into the path of Kone.
After the Ivorian striker was pin-balled between the two defenders he managed to keep control of the ball to prod the ball to Howard's right and into the net from six yards.
The game began to get scrappy towards the end, with both sides searching for another goal.
Latics best chance fell to James McCarthy but it was only half a chance as Caldwell teed him up inside the area, only for the Republic of Ireland international to fire over the angle of the bar and post.
It was a feisty Boxing Day encounter and a close one but, Everton just about edged it.
The travelling Wigan Athletic support deserves a special mention though, as they remained in fine voice for 90 minutes with the 'Banana Army' in full swing.