Rangers booked their place in Thursday afternoon's Petrofac Training Cup quarter-final draw with a 2-0 win over Ayr United at Somerset Park.
Nicky Clark and Barrie McKay scored first-half goals for Mark Warburton's team as they continued their good start to the season against their Ladbrokes League 1 opponents.
Elgin City caused an upset at the Indodrill Stadium, beating Alloa 2-0 after extra time. Craig Gunn and Marc McKenzie got the goals for Jim Weir's men, both of them from the penalty spot.
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