The Bucks were far from their best in the first half and, deservedly, went into the break a goal down - Connor Dimaio making them pay for some unsure defending.
Gavin Cowan's charges could have - and probably should have - been two or three down by the hour mark at the New Bucks Head, but they kept plugging away and their perseverance was rewarded as Cowans got his first of the season.
They are third in National League North, 10 games in.
Telford announced the signing of left-back Callum Cockerill-Mollett, on loan from Walsall, an hour before kick-off and he went straight into the starting line-up. The 19-year-old was in for Dom Smith.
Up against powerful runner Adam Thomas, he endured a harsh introduction to life with the Bucks - mistiming a few tackles and giving the ball away.
The home side had their moments in the first half. Andre Brown's pace posed problems to the Hatters' high line and he had a couple of efforts. One went high and wide while the other was straight at Ben Hinchliffe.
For the most part though, Telford just could not get into a rhythm. Stockport looked to be moving the ball a second or two quicker.
Bucks goalkeeper Max Bramley was not his usual commanding self either. He did well to deny a couple of Frank Mulhern attempts but an unsure punch following a corner was capitalised upon as the visitors took the lead. Dimaio still had a fair bit to do but made it look easy, finding the top corner from 18 yards.
Bramley, in hindsight, should have caught the cross. And the on-loan glovesman gave fans another heart-in-mouth moment just prior to half-time. He rushed off his line to tackle Darren Stephenson. Bramley did not get the ball but the referee, fortunately, did not penalise him. Instead, he booked Stephenson for diving.
The Hatters came out of the traps fastest after the break as well. Stephenson was allowed the time and space to drive at the Telford defence and his cross found Mulhern, whose acrobatic strike smacked the woodwork.
While the Bucks were not free-flowing in open play, they were still troubling Stockport from set pieces. Darryl Knights' free-kick, nine times out of 10, would have gone in. This time though, Hinchliffe pulled off a miraculous save with his fingertips.
Such a fine piece of goalkeeping suggested Telford would not be able to come up with an equaliser. But they did just before added-on time as Cowans poked in following some fine work from substitute Matthew Barnes-Homer.
Cowan was determined to see a response from the Bucks after the losing their previous outing 3-0 at Darlington - and the character they showed to grab a point should be applauded.
34 - Goal! Telford 0-1 Stockport. Connor Dimaio nets for the away side, who have been knocking on the door for several minutes. A corner is punched away by Max Bramley but only as far as Dimaio. He sublimely curls home from the edge of the box.
47 - Almost a nightmare start to the second period for the Bucks. Frank Mulhern smacks the crossbar with an overhead kick.
50 - WHAT A SAVE! Darryl Knights' free-kick is, somehow, tipped onto the bar by Ben Hinchliffe. Top-drawer goalkeeping.
88 - GOALLLLLLLLL!!!!!!!!!!! Telford 1-1 Stockport. Henry Cowans levels for the hosts. Matthew Barnes-Homer's ball across the face of goal deflects towards Cowans, who back-heels it in.
Telford (4-4-2): Bramley; White, Sutton (c), Streete, Cockerill-Mollett (Dawson, 67); Cowans, Deeney, McQuilkin (Royle, 67), Knights; Udoh, Brown (Barnes-Homer, 73)
Subs not used: Smith, Wycherley (gk)
Stockport (4-4-2): Hinchliffe; Minihan, Palmer (c), Cowan, Duxbury; Thomas, Keane, Walker, Dimaio (Warburton, 62); Mulhern (Bell, 62), Stephenson (Kirby, 79)
Subs not used: Mantack, Ormson (gk)
Referee: Michael Barlow (Lancashire)