Hearts and Dundee United have advanced to the Scottish League Cup’s last 16 with wins, and the other top-flight team St Mirren need a point to join them.
Liam Boyce and Finlay Pollock’s goals against Stirling Albion confirm Hearts’ position as Group A winner.
Peter Pawlett, meanwhile, scored before half-time to beat United past East Fife to secure a fourth of four win.
A goal from Thomas Orr of Stenhousemuir scared St Mirren, but they scored three of their own to win.
Cove’s Ligue 1 Rangers surprised championship team Inverness Caledonian Thistle, with two goals in three minutes from Leighton McIntosh and Mitchell Megginson to which was added the efforts of Blair Yule.
He leaves just two points between second and fifth in Group A, although only Stirling and Inverness can hope for a better second place.
Ayr United took the kick off of the night with a Cameron Salkeld goal against Hamilton. Four of the five teams in Group E could still finish first before the last round of games.
Kilmarnock earned a potentially invaluable bonus point, beating championship rivals Morton 4-2 on penalties after Kyle Connell’s goal called off 17-year-old Lewis McGregor’s opener for the Greenock side.
Clyde won 4-2 on penalties in the other Group G game after Lowland League East Kilbride held them at K-Park. This means that Clyde, Kilmarnock and Stranraer enter the final match with hopes of winning the group.
Kelty Hearts also gave himself a chance to fight for a better second place in the Dundee United squad after coming back from behind to beat Elgin City.
Queen’s Park’s 2-1 win over Annan Athletic means Motherwell can win Group F on Wednesday against the Airdrieonians. Laurie Ellis’ side currently lead the group with two points, but have played all of their games.
Partick Thistle beat Dumbarton 2-0 in Group H but needs a substantial win over St Mirren if he is to progress.
Scottish League Cup results
Cove Rangers 3-1 Caledonian Thistle Inverness
Stirling Albion 0-2 Hearts
East Fife 0-1 Dundee United
East Fife 1-3 Kelty Hearts
Brechin City 1-0 Alloa Athletic
Hamilton Academical 0-1 Ayr United
Annan Athletic 1-2 Queen’s Park
East Kilbride 2-2 Clyde (2-4 pens)
Kilmarnock 1-1 Greenock Morton (4-3 pens)
Stenhousemuir 1-3 St Mirren
Partick Chardon 2-0 Dumbarton