They actually led for 53 minutes with a Louis Moss goal, but the turning point was a second half injury to Chris Noone.
He had to be helped off with a badly twisted ankle and the enforced change disrupted the side long enough for Stockport to equalise.
After making a better start than the home side, Colwyn Bay took the lead after 17 minutes.
Ob Anoruo, who was captain for the day and did well as a lone front man, broke free on the right and from his cross Paulo Mendes saw his effort to turn the ball into the net blocked by home keeper Danny Hurst – but Louis Moss was following up to score.
It took Stockport 29 minutes to get their first shot at goal, but they put the visitors under huge pressure in the last 15 minutes of the half.
Anthony Stephens, who was brilliant in his final game before returning to Wrexham, cleared off the line from Chris Sharp and Bay keeper Josh Ollerenshaw punched clear a header from Sharp and then blocked a shot from Scott Spencer with his body in a one-on-one to keep the Bay in front at half-time.
Spencer also headed wide from a corner and Glenn Belezika had a goalbound effort blocked away for a corner by Stephens.
In the second half Colwyn Bay looked to be holding their own, but the injury to Noone, after a collision with Stockport’s man of the match Belezika, unsettled them for a while and Stockport capitalised when substitute Chris Churchman blocked an attempted clearance and scored from 25 yards.
The diving Ollerenshaw got a hand to the ball, but not enough to turn it round the post.
To their credit the Seagulls regrouped and after surviving ten minutes of fierce pressure, actually finished the game the stronger with Paulo Mendes having a stinging shot saved by the keeper and Anoruo putting two efforts over the bar.
Manager Frank Sinclair admitted the injury to Noone, who could be a big doubt for Sunday’s home game against Hyde, was a factor in the team losing their lead.
“It seems that little things like that are going against us at the moment,” he said. “But we asked the lads for 100 per cent effort and they gave that, so you can’t ask for more.
“They (Stockport) are a very professional group with more experience than us and when you’ve got such a young group as we’ve got it is really hard to get consistency.
“But I thought we matched them for 60 odd minutes, took the lead and Josh has held his hands up to say he probably should have saved the shot for their goal, so we are bit disappointed not to have go all three points.
“We’ve now got a must win game on Sunday. I wanted four points from the two Christmas games and if we can do that we’ll be a lot happier going into next week.
“Obviously we now lose Anthony Stephens, who has been brilliant, and I am working all the hours there is to try and bring in another centre half, but for now we have to work with what we’ve got.”
Chris Sanna, who was on the bench today, could play his first game on Sunday while Rob Hopley is coming back from injury and is also in line for a possible start.
Colwyn Bay: Ollerenshaw, Taylor, Truelove, Stephens, Royle, Noone (Hopley 67), Moss (Olapade 76), Haywood, Anoruo, Mendes, Baynes. Subs not used: Sanna, Sinclair, Hodgson