The visitors, facing another relegation battle in the Premier League and underdogs in this quarter-final, had effectively booked their place in the last four after 34 minutes following goals from Maynor Figueroa, Callum McManaman and Jordi Gomez.
Defender Figueroa headed Wigan in front from a corner in the 30th minute, former Everton schoolboy McManaman capitalised on Phil Neville's mistake to double the lead 90 seconds later, and Gomez, the Spanish midfielder, made it three with an exquisite left-foot curler from 20 metres.
Manchester City are aiming to join Wigan in the semi-finals when they host Barnsley of the Championship (second division) later on Saturday. On Sunday, Millwall face Blackburn Rovers in an all-Championship tie and Manchester United meet Chelsea in the remaining sixth-round match.
Both semi-finals will take place at Wembley on the weekend of April 13 and 14.