Holders Rangers will take on Celtic in the semi-finals of the Scottish Cup next month.
League One side Falkirk, who beat Ayr United 2-1, will face another Championship side Inverness in the other last-four tie.
The Highland club were initially knocked out of the competition by Queen’s Park in the fourth round before the Glasgow outfit were ejected for fielding an ineligible player.
Inverness won the trophy for the first time in 2015 when they beat Falkirk in the final.
Celtic beat Rangers in last month’s Viaplay Cup final at Hampden Park.
The ties will take place on the weekend of April 29-30.