The Portuguese wide player finished well for the opener before producing the strike that allowed Liel Abada to net on the rebound.

David Turnbull then notched his sixth goal of the season before Dario Zanatta was sent off just before the hour mark.

Celtic comfortably saw out the game against the cinch Championship side without ever threatening to move up the gears.

Postecoglou made three changes to his starting line-up following defeat at Livingston, all in the back four. Anthony Ralston, Carl Starfelt and Adam Montgomery came in to join Cameron Carter-Vickers.

James McCarthy retained his place after his inauspicious first start in West Lothian and spent a fair part of an uneventful first quarter apologising to teammates over misplaced passes.

The Republic of Ireland midfielder redeemed himself with a brilliant reverse pass to set up Jota for the opener in the 26th minute. The on-loan Benfica winger got a run on Reghan Tumilty and found himself beyond the Raith back four before raising his shot above the diving Jamie MacDonald.

Joe Hart soon made his first save, from Aidan Connolly, after Celtic lost possession while playing it around deep in their own half.

Jota was heavily involved in the second goal five minutes before half-time. The wide player beat his man and fired a powerful strike that MacDonald could only parry into the path of Abada, who nodded home.

Celtic moved further ahead two minutes into the second half. Albian Ajeti tracked back to regain possession near the halfway line to allow Turnbull to stride forward and stroke a curling effort into the net from 25 yards.

Tom Rogic shot straight at MacDonald from a decent chance before the odds stacked further against the visitors when Zanatta picked up two yellow cards inside five minutes. After being booked for a foul on Rogic, the winger was sent off in the 59th minute for pulling back Ralston.

It was not all good news though for Postecoglou, who revealed afterwards he had suffered more disruption to his forward line after new striker Giorgos Giakoumakis suffered a calf injury during the warm-up which caused enough concern for him to be sent for tests.

Winger Mikey Johnston was also missing after picking up a minor injury in training days after returning from a hamstring problem to make his first appearance of the season at Livingston.

On Giakoumakis, Postecoglou said: "We have sent him off for a scan. There's something looming over me at the moment just to challenge me every day and we will just have to cope.

"It has been challenging but we just have to work through it and build resilience. We went through the first period of the season really short at the back and now I think I had four full-backs and three centre-backs out there.

"Now we have some great players in the front line but we can't get them on the field."

Celtic next take on holders St Johnstone in the semi-finals which will which take place on November 20-21.

Steven Gerrard's Rangers will meet Hibernian in the other tie after the Leith side beat Dundee United 3-1 at Tannadice.

Australian Associated Press