The two sides ended 120 minutes locked at 1-1 at a sun-drenched Wembley, before the Cumbrians prevailed thanks to perfect spot-kicks from Kristian Dennis, Jon Mellish, Ryan Edmondson, Owen Moxon and Taylor Charters.
Ryan Rydel’s sole missed attempt for Stockport prevented them from sealing back-to-back promotions, while Carlisle lapped up their triumph in what was their first-ever play-off final.
In perfect summery conditions and in front of a crowd of over 34,000, it was Stockport who threatened first when captain Paddy Madden’s header looped onto the roof of the net.
The Hatters, featuring two changes from their semi-final second-leg triumph against Salford, bossed the possession in the opening 23 minutes, but neither side managed to create anything further in front of goal.
That was until Carlisle, without semi-final tie-winner Ben Barclay as he is on loan from Stockport, almost struck the first blow.
Joe Garner leapt superbly to meet Moxon’s free-kick into the box, but his header was expertly palmed around a post by goalkeeper Ben Hinchliffe.
The conditions were proving tough and energy-sapping, but it was Stockport who made the breakthrough – courtesy of a large slice of fortune – in the 34th minute.
Striker Isaac Olaofe appeared content to simply swing in a cross from wide out on the right, but the ball clipped heavily off the boot of Mellish before looping over keeper Tomas Holy and finding the far corner.
Cue wild celebrations in the Stockport half of the stadium, but they were almost pegged back in first-half stoppage time.
John-Kymani Gordon barged past the challenges of Chris Hussey and Akil Wright, only to then fire over from 15 yards.
The opening 10 minutes of the second period were equally as cagy as the early stages of the first, with so much at stake, but Stockport fluffed a terrific chance to notch again shortly before the hour mark.
Wright darted in unopposed to meet Hussey’s cross, only to somehow head wide from eight yards.
County substitute Myles Hippolyte then went close with an acrobatic scissor kick as his side continued their search for a potentially victory-clinching second goal.
At the other end there were loud penalty appeals when Mellish’s shot was blocked by the armpit of Kyle Knoyle, but that was soon forgotten as the Cumbrians went on to grab an 84th-minute leveller.
Substitute Omari Patrick sent the tie into extra time, drilling home after Joel Senior’s low cross was not dealt with by the Stockport defence.
After Jack Stretton, for Stockport, and Carlisle’s Dennis had both gone mightily close to settling it in the extra period, it was left to Paul Simpson’s men to seal their promotion thanks to their handful of faultless spot-kicks.
