The visitors started the game strongly and Roger Espinoza latched onto a throw-in from Maynor Figueroa, and was allowed space and time to drill a volley at goal, but Jack Butland was on hand to make the stop.
Wigan continued to have the better of the opportunities in the early going as they frustrated the home side, and Adam Forshaw's drive from 25 yards went just over the bar, with Butland scrambling.
Uwe Rosler's men went close again as Callum McManaman fired an effort at goal from close range, but Butland came out to narrow the angle and made an impressive block with his body to keep the scores level.
Wigan were handed a glorious chance to take the lead just before the break when Eustace was adjudged to have handled the ball inside the area. James Tavernier took the spot kick, but saw his effort saved by Butland.
Derby immediately raided downfield and won a free kick from which Johnny Russell lifted a dangerous cross into the area that was volleyed into the net by Eustace.