Wigan, who had beaten three Premier League teams in the Cup including Manchester City in the previous round, could not convert their chances, however, and Southampton came out strongly after the break.
The decisive goal came in the 62nd minute when Hojbjerg converted with a side-foot finish from a Dusan Tadic corner.
Southampton had a chance to wrap up the tie when they were given a penalty with 18 minutes remaining but Manolo Gabbiadini's spot kick, awarded after he had been brought down by Dan Burn, was brilliantly saved by Wigan keeper Christian Walton.
Southampton's second goal came in injury time when Soares finished off a swift counter-attack, led by Nathan Redmond, with a calm finish into the far corner.
Southampton join Tottenham, Manchester United and the winner of Sunday's other tie between Leicester City and Chelsea in the semi-finals.
(Reporting by Simon Evans; Editing by Toby Davis)
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