Dundee were rarely troubled as they swept aside Morton 5-1 in the fifth round, and they will play a United side who booked their progression with a comfortable 3-0 win over Rangers on Saturday.
Celtic have been offered the chance of gaining quick revenge after being drawn away to St Mirren, who knocked the Hoops out of the Scottish Communities League Cup at the semi-final stage last month.
A team from the Irn-Bru First Division will be represented in the last four after Hamilton drew a home tie against Falkirk, while the remaining quarter-final sees Hibernian visit Kilmarnock.
The ties will be played on the weekend of March 2-3.
- Sports & Recreation
- St Mirren