Alan Forrest, brother of Celtic winger James Forrest, took advantage of a mistake by Gers keeper Wed Foderingham to give League One side the lead.
James Forrest scored a hat trick as Celtic overcame Partick Thistle 3-2 in their Scottish Cup fifth-round clash at Parkhead.
Josh Windass' hat-trick gave Rangers a 3-0 victory as they produced a professional display to dispatch Fraserburgh from the William Hill Scottish Cup.
Holders Celtic eased into the fifth round of the Scottish Cup with a 5-0 home win over struggling Brechin.
Pedro Caixinha has launched an astonishing attack on his Rangers players after their Betfred Cup semi-final loss to Motherwell.
Brendan Rodgers is now just 90 minutes away from joining Celtic's elite band of treble-winning bosses after his team beat Rangers 2-0.