Both of the top two drew in Saturday's Scottish Premiership matches with league leaders Celtic failing to score against Kilmarnock.
The Bhoys had 20 shots but were only able to test Killie goalkeeper Jamie MacDonald five times at Celtic Park in their 0-0 draw.
Arnaud Djoum struck in the first half to give Hearts the lead but Dundee striker Rory Loy equalised with 23 minutes remaining.
St Johnstone had to come from behind to triumph in the Tayside derby. Billy McKay gave Dundee United the lead but goals from Christopher Kane and Murray Davidson handed the Saints the points.
Elsewhere, Partick Thistle came from behind to beat Inverness Caledonian Thistle 2-1, and Craig Curran scored the opener as Ross County defeated Motherwell 3-0.
Aberdeen will play Hamilton Academical on Sunday afternoon.
Results in full (half-time results in full): Celtic 0-0 Kilmarnock (0-0), Dundee United 1-2 St Johnstone (1-2), Hearts 1-1 Dundee (1-0), Partick Thistle 2-1 Inverness Caledonian Thistle (1-1), Ross County 3-0 Motherwell (1-0)
