Five minutes into the extra period after a stalemate during normal time, the Morton player scored from the spot after referee Bobby Madden adjudged Celtic defender Efe Ambrose to have handled when challenging substitute Archie Campbell.
Celtic, who had been lacklustre for most of the game, pounded the Morton goal in an attempt to get back level and Charlie Mulgrew hit the post in the dying seconds.
However, on night of unlikely drama, the resolute visitors were not to be denied.
With the top tier of the stadium closed and the rest of the ground far from full, the first half was pretty uneventful not to say uninspiring.
Mulgrew, playing at left-back in a reshuffled Celtic side, came closest to scoring with a free-kick which was tipped away for a corner by Ton’s French goalkeeper, Nicolas Caraux.
However, Morton, second-bottom of the Scottish Championship, defended stoutly for the rest of the 90 minutes without offering much of a threat in attack but Imrie’s penalty was all they needed.
Celtic manager Neil Lennon had noted beforehand that he had not yet won this trophy as a manager and he will have to wait at least another year. The defeat also put an end to any hopes of Celtic winning a treble this season.
In the other third-round ties played last night, the three Scottish Premiership sides made comfortable progress.
Liam Craig completed his first-ever hat-trick as Hibernian clinched a quarter-final slot with a 5-3 win over Stranraer at Easter Road. Hibs’ summer recruit Abdellah Zoubir also found the net and Stranraer’s Scott Rumsby scored an own goal. Stranraer got on the scoresheet thanks to Chris Aitken and a Michael Nelson own goal.
At Dens Park, Billy McKay netted his seventh goal of the season to give Inverness Caledonian Thistle a 1-0 win over Dundee. But Terry Butcher did not believe his team deserved the win.
“If we go play like that against Hibs on Saturday we will be turned over,” said Butcher. “Fair play to Dundee – they deserve to go through and not us. They bossed the game. I told Bomber [Brown] that his side were excellent and deserved to go through.”
At New Douglas Park, St Johnstone beat Hamilton Accies 3-0.
Stevie May returned to haunt his former club as he scored a double, while Gwion Edwards came off the bench to claim his first goal for the club.