The Capital club defeated Kilmarnock 2-0 at Easter Road on Sunday as they reacted positively to Thursday night’s Europa Conference League exit.
Goals from Kyle Magennis and Kevin Nisbet were enough to see Hibs through to the next round although Killie hit the bar through Liam Polworth and tested Matt Macey in more than one occasion.
Tam Courts’ side needed penalties to eliminate Championship Ayr United on Saturday but now host the Hibees for a place in the semi-finals.
Hibs could be backed by a large travelling support, with football stadia expected to be back operating at full capacity by the time the League Cup matches come around again.
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Elsewhere in the draw Celtic host Raith Rovers, Rangers will play Livingston, and Dundee take on St Johnstone.
Fixtures will take place during the midweek of September 21-23.