The pair were due to play each other for what is now branded the SPFL Trust Trophy in the last edition of the competition in 2019/20 but shared the silverware after the final was cancelled due to coronavirus.
A hat-trick from Billy Mckay helped Scottish Championship leaders Inverness recover from two down to defeat League Two side Elgin 4-2.
Elgin led 2-0 after just over 20 minutes through Tom Grivosti and Brian Cameron but a double from Mckay saw Caley Thistle go in level at the break.
Mckay completed his treble halfway through the second half and Lewis Jamieson produced a fine finish in the 72nd minute to give the visitors breathing space.
Raith were 3-1 winners over East Fife at Stark’s Park. They had the better of three quick-fire goals late in the first half, with Dylan Tait and Aidan Connolly netting either side of a goal for Scott Mercer before Matej Poplatnik added a third in the second half.
There was a remarkable finish to the clash between Cove Rangers and Albion Rovers, which was goalless heading into the 79th minute but ended 4-1 to the hosts.
Mitchel Megginson, a double from Rory McAllister and Jamie Masson gave Cove four goals in 10 minutes before Maxwell Wright grabbed a consolation for League Two Albion.
Greenock Morton edged past Montrose 4-2 on penalties, Gary Oliver scoring the winning spot-kick after a goalless draw.
Two third round matches took place on Friday night.
Kilmarnock eased past Queen’s Park 3-1 at Rugby Park with goals from Oli Shaw, Euan Murray and Callum Hendry after Grant Gillespie had equalised from the penalty spot for the League One leaders.
Meanwhile, in Dumfries, Queen of the South overcame Championship rivals Partick Thistle thanks to goals second half goals from Lee Connelly and Ally Roy, the latter’s strike coming in the 92nd minute.
Hamilton also reached the quarter-finals courtesy of a 2-0 win over Aberdeen on Wednesday. The final third round clash takes place on Wednesday, October 27 when Alloa Athletic host Rangers B.