The Premier League visitors were the dominant side from the first whistle, but it took them until the 31st minute to break the deadlock.
Winger Callum McManaman dribbled the ball into the Huddersfield area and despite a narrow angle, he managed to lift the ball over Alex Smithies and into the roof of the net.
He then turned provider as Wigan extended their lead five minutes before the interval. His cross caused uncertainty in the Huddersfield defence and Arouna Kone was on hand to bundle the ball over the line.
Should Wigan hold out in the second half, they will become only the second top-flight team along with Manchester City to secure their spot in the quarter-finals of the competition.