Holders Celtic coasted into the semi-finals with a 5-0 home win over Partick Thistle thanks to goals from Vakoun Bayo, Tom Rogic, Olivier Ntcham (2) and Scott Sinclair.
Rangers got the better of Livingston as Glen Kamara's early goal at the Tony Macaroni Arena proved decisive in a 1-0 victory for Steven Gerrard’s men.
Hearts beat Aberdeen 3-0 on penalties after a 2-2 draw at Tynecastle. Sam Cosgrove converted two spot-kicks for the Dons but the hosts equalised late on through Craig Halkett after Steven MacLean had scored in the first half.
Kilmarnock and Hibernian drew 0-0 at Rugby Park, with Hibs winning 5-4 on penalties.
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