An even, see-sawing game saw the balance of power shift several times, before a late, late goal from Nathan Wolfe stole the points for the home side.
Defending from set pieces saw Danny Glover add to the number of teams he's played for when scoring against Celtic, getting a great deal of power on Stephen O?Hallaran's nod back across face from a whipped in corner, Lewis King was further wrong footed by the shot taking a slight deflection.
But the balance soon shifted, and when Stephen Brogan's lifted ball saw Celtic's new wunderkind, Jonnie Allen, outpaced the entire and keep his cool and calm facing down Danny Hurst to roll the ball past him and equalise.
Allen went agonisingly close to giving Celtic the lead moments later when his low shot skimmed the wrong side of the upright. Stockport too went close, O?Halloran's effort was blocked, and Kristian Dennis's effort was a routine stop for King, while at the other end a Ben McKenna whipped in cross was nodded goalward by Allen, but well stopped by Hurst, before McKenna himself cut inside from the wing and tried his luck, firing wide of the mark.
The second half started off with Celtic in the ascendancy, Paul Ennis and Allen both frustrated by a massed Stockport defence and Scott Kerr's twenty-yard effort was just over.
So it was somewhat against the run of play that Stockport got their nose back in front, a half cleared ball in was latched onto by Danny Glover who's stabbed home ball gave the advantage to the Hatters.
But Celtic were still playing well, and Allen's initial effort could only be parried by Hurst, with McKenna following in to fire home from close range.
Celtic's ascendancy continued after the equaliser, and got them in front as McKenna turned provider for Allen racing in, to score his second and Celtic's third.
With less than twenty minutes remaining, Stockport threw everything at Celtic, and got the equaliser their pressure deserved, an uncleared free kick coming to Kristian Dennis twenty-yards out, who fired on the turn into the top corner.
Celtic twice went close to regaining the lead as stoppage time approached, new signings Michael Potts firing over, and Charlie Dawes forcing Hurst into a half decent stop, before Dawes clashed with Tunji Moses, some distance out, but the ball into the mix was headed home by Nathan Wolfe with just seconds left on the clock, ending what had been an entertaining match that Celtic will have to feel aggrieved they took nothing from. It augurs well for the forthcoming games however, as Celtic did play very well.