Five minutes into the extra period after a stalemate during normal time, the Ton midfielder 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, put pressure on the Morton box in an attempt to get back level and Charlie Mulgrew hit the post in the final seconds.
Liam Craig completed his first ever hat-trick as Hibernian clinched a Scottish League Cup quarter-final slot with a 5-3 win over Stranraer.
The former St Johnstone midfielder kept a clear head to net a fine treble with Abdellah Zoubir also netting for Hibs in addition to a Scott Rumsby own goal.
Jamie Longworth and Chris Aitken scored for Stranraer with a Michael Nelson own goal following.
Billy McKay netted his seventh goal of the season to send Inverness into last eight with a 1-0 win over Dundee.
McKay had already threatened with a shot over the bar before giving Caley Thistle a ninth-minute lead at Dens Park as they bounced back from their first defeat of the season against Aberdeen.
Stevie May returned to haunt former club Hamilton as he bagged a double to send St Johnstone into the quarter-finals with a 3-0 victory.
May, who spent last season on loan with Accies, grabbed the opener early on in the tie at New Douglas Park.
Gwion Edwards then came off the bench to claim his first goal for the club late on, before May struck again in injury-time.