The winger was handed the left-wing berth 24 hours after McGeady completed his £9.5million move to Spartak Moscow and he repaid Neil Lennon in style in the 56th minute as Celtic recovered from a slow start to produce a commanding second-half display in Saturday's season opener at the Caledonian Stadium.
McCourt beat three men before finishing brilliantly in a goal reminiscent of his solo efforts against St Mirren and Falkirk last season, although he paid the price as he suffered a head knock that ended his involvement.
Lennon would have been equally pleased to see his defence keep their first clean sheet since the summer break, a run that included eight friendlies and two Champions League games against Sporting Braga.
Lennon, who was able to field injury concern Scott Brown from the start, had brought his players to the Tulloch Caledonian on Friday to acclimatise them to what were unfamiliar surroundings for many. But they looked like strangers to each other as Irn-Bru First Division champions Inverness dominated the opening stages.
Jonny Hayes almost burst straight through the Celtic defence in the opening minute before Glenn Loovens cleared and Inverness created the first shooting chance when Adam Rooney volleyed Kevin McCann's cross a yard wide.
Charlie Mulgrew resorted to a crude block on Hayes shortly after being beaten on two occasions by the winger and Celtic took almost 15 minutes to threaten only for McCann to foil McCourt following Cha Du-ri's cutback.
Russell Duncan soon tested Lukasz Zaluska with a 25-yard drive at the other end and Hayes was causing Celtic a major headache, with Eric Odhiambo heading his cross over after a sharp build-up.
However, Celtic missed a great chance in the 21st minute after Georgios Samaras played strike partner Shaun Maloney clean through. The Inverness defence stood waiting for a flag that never came but Maloney struck the top of the post from 15 yards with only Ryan Esson to beat.
Inverness bounced back from the let-off and Rooney glanced over after impressive wing play from Nick Ross before they created their best chance in the 32nd minute.
Hayes beat two men to the ball inside the box before helping it into the path of Rooney, whose low shot was blocked by Zaluska.
The game was now flowing from end to end and Inverness debutant Kenny Gillet blocked shots from both Fortune and Joe Ledley after a low cross by Samaras, who soon had several opportunities himself, the best of which saw Ross block his header on the line following Mulgrew's corner.
Esson ensured the half was goalless in injury-time when he blocked Fortune's near-post effort with his defence stretched and the Inverness goalkeeper was busy immediately after the interval too.
He stretched to push past Mulgrew's 25-yard free-kick before standing firm as Ledley ran on to Maloney's defence-splitting pass to drive a shot from 20 yards.
Celtic soon went ahead as McCourt added to his collection of brilliant individual efforts and the visitors' threat was not diminished after James Forrest came on for the injured goalscorer.
Celtic took complete control and Scott Brown saw a shot held after a driving run before Ross Tokely cleared Maloney's effort off the line after Fortune had retrieved a Mulgrew cross.
Samaras burst down the left and shrugged off Tokely before seeing Esson block his ambitious effort and soon set up Maloney, whose shot again beat Esson but drifted inches wide of the far post.
Celtic continued to push forward and Esson scrambled clear Maloney's flick before Forrest blazed over from 10 yards after a Fortune cutback.
Forrest later produced two much better efforts from long range, the first tipped wide by Esson and the second crashing off the bar.
Inverness, who saw Gil Blumenshtein limp off shortly after coming on, never looked like getting back in the game as Lennon made it nine consecutive SPL wins as manager.