Ryan Porteous scored the winning penalty when Hibernian knocked Motherwell out of last year's tournamentThe Old Firm head to Tayside in Scottish Cup quarter-final action as Dundee United host Celtic and Dundee welcome Rangers.
Hearts, third in the Scottish Premiership, have a home draw against sixth-placed St Mirren.
Beaten 2021 finalists Hibernian travel to Motherwell as they aim to go one better than last season.
The ties, contested exclusively by top-flight clubs, take place on the weekend of Saturday, 12 March.
Scottish League Cup winners Celtic are on a 10-game unbeaten run since lifting the first silverware of the season in December, beating Hibs 2-1 at Hampden.
Ange Postecoglou's league leaders edged Dundee United with a 90th-minute winner when the sides last met on 29 January.
Rangers cruised into the last eight with a heavy win over League 2 Annan Athletic, but have been usurped at the Premiership summit, trailing Celtic by a point.
They travel to Dens Park after Dundee overcame an impressive Peterhead side in the final last-16 tie on Monday night.
Hearts, who lost the delayed 2020 final to Celtic on penalties, required a shootout themselves to see off Livingston on Saturday.
They are due to face St Mirren, winners against Ayr United, away on league business on 26 February before hosting them in the cup.
Motherwell, who defeated Aberdeen 2-1 in the fifth round, and Hibernian, winners against Arbroath on Sunday, were quarter-final opponents last season at Easter Road, with Hibs prevailing in the shootout after the match finished 2-2.
Full draw
Heart of Midlothian v St Mirren
Dundee United v Celtic
Dundee v Rangers
Motherwell v Hibernian
Ties to be played on weekend of 12 March.
