A deflected strike from Leon Osman and a Phil Jagielka header, both in the second half, proved enough for the Toffees in a rain-sodden Barclays Premier League encounter despite a late reply from Arouna Kone.
Wigan felt they should have had a penalty soon after Osman's opener but luck was against the Latics, who remain in the bottom three despite another spirited showing.
The Toffees recorded their second win of the festive season - and extended their unbeaten Barclays Premier League run to seven games.
It kept them joint fourth in the table, just two points behind third-placed Chelsea, their opponents on Sunday.
Moyes said: "Over the Christmas period you are just trying to win the games and come out of the other end of it in no worse a position.
"We have six points from the two games and we might have settled for that at the start but we have now got another couple of games - Chelsea at home and then Newcastle away - and then you are probably talking about the Christmas period being over.
"We will try to take some points from them and keep moving up."
Moyes said: "Wigan played well and I have to give them credit.
"They will do the same to most teams and they don't get enough credit for the way they pass the ball and the way they play.
"I thought before half-time we were starting to look the better side but we are never comfortable because of the way Wigan play.
"We just raised it a bit at half-time and it made the difference.
"The big thing was when Ossie (Osman) went into the middle of the park - it made us play better.
"He has got happy feet. He danced through and got a shot away, obviously it took a bit of a deflection.
"The second one was a good header. It was about time a centre-half scored a goal and I'm glad Jags got it."
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Shaun Maloney appealed in vain for the spot-kick after going down in a challenge from Osman.
Replays suggested Maloney may have been falling before contact from Osman but Moyes feared the worst.
The Scot, whose side remain firmly in Champions League contention as a result of the win, said: "From where I was sitting I thought it could be (a penalty) but I have also seen their goal where Kone punches the ball into his path to score.
"I am not saying that is evening it out. My first thought from the bench was: 'this could be a penalty kick'.
Wigan manager Roberto Martinez had no doubt his side, who have now not won in six games, had been hard done to again after also being denied a penalty in last weekend's defeat by Arsenal.
Martinez said: "Shaun Maloney is not a player that looks for penalties.
"He is someone who once he gets in that one v one situation you know how effective he can be.
"He goes past his defender easily and there is no need for him to go down but I think if you look at Leon Osman's reaction it tells you everything.
"If you see defending a one v one in the box and someone goes down, you go mad - and rightly so.
"Leon Osman just went away and showed a face of feeling that he got away with that incident. "I don't really understand what the referee saw and I am getting a bit tired of talking about these moments."
Wigan, after narrow escapes in each of the past two seasons, appear to be heading for another relegation battle.
Martinez feels his side must start making the most of every opportunity because decisions and luck continue to go against them.
He said: "I'm frustrated and angry. It is a moment of the season where results are starting to be very important.
"We knew we were coming to a difficult place but the way we played the first half, I thought we stopped them from having any momentum.
"We were starting to get into a good position to get a positive result and actions in both boxes cost us.
"We need to make sure we don't rely on third parties - we don't rely on decisions to get positive results.
"We will learn from it. It is not good enough just to play well in the Premier League, whichever ground you are playing at.
"If we need to play extra well to get a positive result, that is what we have got to do."
Moyes added that midfielder Darron Gibson was withdrawn at half-time because of a thigh strain.
Gibson could miss the next three games in any case if he fails in an appeal against his sending-off at West Ham last weekend.