Tottenham, without a win in their previous five games, had struggled through the first half against a Wigan side that had won five of their previous six matches.
However, Russia striker Pavlyuchenko's 52nd minute penalty changed the game and the eight times FA Cup winners deserved their place in Sunday's fourth round draw as they maintained their record of never having lost to the north-west club.
Wigan were sharper from the start as Henri Camara flashed a header wide after five minutes but with first-choice strikers Emile Heskey and Amr Zaki missing through injury they struggled to turn possession into clear chances.
Spurs had barely threatened until Gareth Bale's through ball was deflected into the path of substitute Fraizer Campbell and as he pushed it past Richard Kingson, Wigan's debutant keeper brought him down.
Pavlyuchenko sent Kingson the wrong way when he calmly rolled the penalty into the corner of the net.
DANGEROUS PAVLYUCHENKO
Spurs livened up after the goal with Pavlyuchenko looking dangerous and Campbell forcing Kingson into a good save with a powerful header.
Modric then showed quick reactions when, face down on the ground after slipping, he headed in the rebound after Jamie O'Hara's shot came back off a post following an excellent build-up in the 76th minute.
Wigan kept pressing and pulled a goal back three minutes from time when Camara seized on a loose ball to score from close range. Pavlyuchenko, though, had the last word when he cut inside to fire home Tottenham's third in stoppage time.
Spurs manager Harry Redknapp, who won the Cup last season with Portsmouth, was particularly happy with his scorers. "Roman did well today, took his goals well and worked hard for the team so that was encouraging," he told Setanta Sport.
"We played Luka in that central midfield role today for the first time and he showed he was strong enough and certainly good enough to play there, he was terrific."
Wigan boss Steve Bruce said: "We didn't just quite have enough firepower, we can't afford to be without four or five players at a club like ours.
"Hopefully, we'll have most of them back when we play them (Spurs) again in the league in a week or so," he added in reference to the January 11 game at the JJB Stadium.
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