Lee netted his fifth goal of the season in the 86th minute from close range after fellow replacement Danny Cadamarteri picked him out with a cross.
Chances and entertainment had been at a premium until then, with Town's goal ace Jordan Rhodes going closest to breaking the deadlock.
Rhodes, who had hit 12 goals in his previous five outings, headed just past the far post on half-time from Jack Hunt's cross. The Scotland ace also saw a shot from Gary Naysmith's through ball flash just wide.
The Latics' best chance came three minutes earlier when Dean Furman turned the ball back in after Huddersfield had cleared a corner.
Defender Jean Yves Mvoto, who had stayed up, was left unmarked and in the clear, but slipped as he was about to shoot.