Scottish Cup holders Inverness won 2-1 at Motherwell on Saturday, as Dundee Utd, Ross County and Morton also reached the last eight.
A late Kane Hemmings' penalty earned Dundee a hard-fought 2-2 draw against Motherwell at Dens Park.
Linlithgow Rose have become the first Junior side to reach the last-16 of the Scottish Cup after they beat Forfar 1-0.
Aberdeen beat Dundee 1-0 at Pittodrie on Friday to close the gap on Scottish Premiership leaders Celtic to three points.
All four senior Scottish Leagues will kick off on August 6 this year, the SPFL has confirmed.
Dundee have completed the signing of striker Arturo Juan Rodríguez Pérez-Reverte on loan from Cordoba.
Hearts are within three points of second place in the Scottish Premiership after hammering Motherwell 6-0, as Dundee and Kilmarnock also won.
Paul Hartley says injury-plagued Kevin Thomson left Dundee because he could not cope with Premiership football.
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29th May 2016