Hibs will travel to Kilmarnock while Hearts host Aberdeen in the quarter-finals of the Betfred Cup.
Paul Heckingbottom's side reached the last eight despite conceding three times at home to Championship side Morton. They were able to avoid an upset as two goals in extra-time gave them a 5-3 victory.
Their opponents at the next stage also needed extra-time in their match as Dom Thomas' goal finally settled Kilmarnock's clash with Hamilton.
Hearts will face Aberdeen after managing to defeat Motherwell 2-1 in front of the BT Sport cameras on Friday night.
Derek McInnes' side were still playing when the draw was made as the Dons needed a last-minute Andy Considine goal to avoid exiting the competition at the hands of Dundee. Sam Cosgrove's goal in the 103rd minute was enough to set up the clash at Tynecastle.
The ties will be played the midweek of September 24-26.