Both goals came in the first seven minutes, with Hazard setting up full-back Branislav Ivanovic for the opener and then winning a penalty that was converted by Frank Lampard.
Wigan dominated much of the rest of the game and pressed hard for a goal, with Chelsea target Victor Moses, former Blue Franco Di Santo and new striker Arouna Kone all forcing decent saves from Petr Cech, but they could not make the breakthrough.
Hazard was Chelsea's highest-profile signing of the close season and it took the Belgian less than two minutes to show why the Blues splashed out a reported £32million.
He turned another summer signing, Wigan's Ivan Ramis, rather too easily in midfield and played a perfect ball through for the onrushing Ivanovic.
The defender was not in his natural territory but he showed impressive composure to run on and slot the ball past Ali Al Habsi.
Wigan and Ramis' afternoon soon got worse as the former Real Mallorca defender crudely upended Hazard in the penalty area and Lampard tucked away the penalty.
The Latics have endured 6-0 and 8-0 defeats by Chelsea in recent seasons and the DW Stadium must have feared the worst, but those were to be the European champions' only two shots of the first half.
Wigan captain Gary Caldwell found a way of stopping Hazard, chopping down the midfielder to earn himself a yellow card in the 11th minute, but the home side began to settle and dominate possession.
Di Santo, who before the match received Wigan's golden boot award for his seven goals last season, headed just over from an Emmerson Boyce cross, while the home fans felt Cech had handled the ball outside his area but referee Mike Jones disagreed.
In the 38th minute Cech was called upon to make his first proper save from a rasping Moses effort, the winger showing why Chelsea have been pursuing him all summer.
Di Santo had Wigan's clearest opening of the half in injury time when he was played in by Maynor Figueroa but his first touch allowed Cech to close him down and a combination of the keeper and David Luiz cleared the danger.
The influential Shaun Maloney was forced off only three minutes into the second half and replaced by Jordi Gomez, but the pattern of the game did not change.
For all Wigan's pressure, Chelsea came within millimetres of making it three in the 63rd minute as Fernando Torres, who had been very quiet, finally found some space and his shot beat Al Habsi but Ramis redeemed himself a little by clearing off the line.
Chelsea boss Roberto Di Matteo then replaced one new signing with another, Oscar coming on for Hazard, while Kone made his Wigan debut in place of Di Santo.
Oscar showed his pace immediately by sprinting past Ramis and firing in a shot from the edge of the area that flew just wide of the far post.
Gomez had a good chance at the other end when he got his head on a searching Figueroa cross but he did not make the contact he would have wanted and the ball dropped harmlessly behind.
The Spaniard did better with a free-kick from 20 yards out after he was felled by Lampard but Cech was behind his well-struck shot.
Kone, who scored 15 goals in the Primera Division for Levante last season, should really have opened his account in the 84th minute but powered a header wide from Gomez's corner.
And moments later the Ivory Coast international forced Cech into a good save before Gomez acrobatically volleyed the rebound just wide.