Dundee United went top of the Championship with a 2-1 win over Queen of the South secured through Scott Fraser's second-half goal.
Paul McMullan gave Dundee United victory at Inverness CT on the opening day of the Scottish Championship season.
The pressure on Hearts coach Ian Cathro has been cranked up after they were dumped out of the League Cup by Dunfermline.
Dundee and Dundee United will face each other again in the Betfred Cup after being paired together at Dens Park.
Peterhead stunned Hearts 2-1 in the Betfred Cup group stage on Tuesday, while Albion Rovers beat Hamilton on penalties.
Kyle Lafferty continued his bright start to life at Tynecastle with a well-taken double against East Fife in the Betfred Cup.
Dundee United came from behind to beat Falkirk and reach the Scottish Premiership play-off final.
Motherwell secured their Premiership survival at the expense of Hamilton on the back of a 3-1 win over Kilmarnock.
| # | Team | Pl | GD | Pts |
|---|---|---|---|---|
| 6 | Dumbarton | 3 | -1 | 2 |
| 7 | Livingston | 3 | -2 | 2 |
| 8 | Brechin | 3 | -4 | 1 |
| 9 | Falkirk | 3 | -4 | 1 |
| 10 | Inverness | 3 | -5 | 1 |
| # | Team | Pl | GD | Pts |
|---|---|---|---|---|
| 1 | Falkirk | 4 | 12 | 12 |
| 2 | Inverness | 4 | 2 | 8 |
| 3 | Stirling | 4 | 1 | 7 |
| 4 | Brechin | 4 | -8 | 2 |
| 5 | Forfar | 4 | -7 | 1 |
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