The Easter Road club have already turned down two bids from Championship rivals Rangers for the highly-rated Scotland Under-21 international, who upped the ante by handing in a transfer request earlier this week.
Allan did not feature in the Petrofac Training Cup defeat by Rangers last Saturday but he made his mark this weekend, finding the bottom corner in the 70th minute just five minutes after being introduced.
Scott Martin (33) had opened the scoring with his first goal for the club, while Jason Cummings added a late third on his birthday to ensure Alan Stubbs’ side joined capital rivals Hearts in the draw for the second round.
Elsewhere, Dunfermline wasted no time in getting up to speed as they romped to a 5-1 win against fellow Fifers Cowdenbeath – with Faissal El-Bakhtaoui and Shaun Byrne both bagging braces – while down the road in Kirkcaldy, Raith Rovers also enjoyed a comfortable afternoon, putting three past Albion Rovers without reply, Lewis Vaughan Kyle Benedictus and Rory McKeown the scorers.
The tie of the round was at Annan where Derek Lyle hit an extra-time winner as Queen of the South secured a dramatic 4-3 win while the hosts finished with nine men.
Queens appeared to be heading out of the competition but Dale Hilson pounced in the third minute of injury-time to force the additional 30 minutes. Kyle’s scrambled winner (100) was book-ended by red cards for Steven Black and Kyle Jacobs
David Banjo scored an extra-time winner as Berwick Rangers came from two goals down to beat Championship side Alloa Athletic 3-2, while another Championship side fell by the wayside as East Fife beat Dumbarton 4-3 on penalties after the game had finished 1-1. Stranraer defeated Stenhousemuir 2-0 thanks to Craig Malcolm’s double.
Ayr United defender Gerry McLauchlan helped knock former club Brechin City out of the competition, with Paddy Boyle also scoring in a 2-0 win.
Jordan Morton’s first-half strike handed Airdrieonians a 1-0 win over Stirling while goals from former Aberdeen stalwart Derek Young, 35, and Danny Denholm helped Forfar clinch a 2-0 victory over Queen’s Park.
Livingston got the better of Clyde for a second successive Saturday as they won 1-0 after extra-time; Livi prevailed in the Petrofac Training Cup by the odd goal in three seven days ago and Jordan White’s winner proved decisive this time around.
On Friday night, Falkirk swept past East Stirling 5-0, while Hearts beat Arbroath 4-2 the night before.