Stockport were looking to feed off of the lively home crowd but it was the visitors that were on top in the first half.
They had their first chance of the game when Matt Smith was left unmarked as he headed straight into the hands of Ben Hinchliffe. An identical move came minutes later – Ibou Touray’s cross fell to Callum Hendry but he couldn’t get past the Stockport ‘keeper.
With half-an-hour on the clock, Paddy Madden nearly got his eleventh of the campaign but he glanced his header wide.
Salford have been superb away from home this season and they had another chance when Stevie Mallan’s shot from outside of the box fell to Smith but his shot was saved.
Stockport thought they opened the scoring when Madden headed onto the top of the crossbar but, despite appeals from all around Edgeley Park, the ball didn’t cross the line.
The Ammies continued to dominate after the interval and pacey winger Luke Bolton came close when he timed his run to perfection but Hinchliffe was on hand again to save.
On the hour-mark, Dave Challinor made three substitutions to try and find that goal they needed.
The Hatters found their goal on the 68-minute mark as Isaac Olaofe angled in a powerful header from Ryan Rydel’s terrific cross.
In the sunshine of Greater Manchester, both teams would have started to have feel the heat get to them, but Bolton certainly didn’t show it.
With moments left to play, the former Manchester City youth player went on a miraculous run from inside his own half, passing a number of Stockport players, but Antoni Sarcevic cleared his effort off of the line.
Five minutes into extra-time, Madden had another chance to take the lead but he was unable to make a clean connection from Rydel’s cross. Two minutes later, their opponent had a chance of their own as Louie Barry looped the ball over Hinchliffe but Chris Hussey cleared away.
With ten minutes of extra-time left, midfield maestro Mallan silenced the home faithful with his effort from range which deflected off of Fraser Horsfall and into the net.
However, the decibel levels rapidly increased when substitute Stretton headed home at the back post to level the aggregate score.
Following a few tense minutes near the end, neither side could find the winner – penalties awaited.
Matty Lund skied his effort over in the first spot kick and Madden stepped up next and made no mistake in dispatching his effort.
Salford’s start to penalties went from bad to worse when Mariappa’s shot was saved. Alex Carins kept his side in the tie however when he saved from Ryan Croasdale.
Louie Barry took the Ammies’ third penalty and he slotted home. Will Collar showed composure as he was next to score and Hinchliffe saved Mallen meaning Sarcevic had the chance to win the tie.
He rifled his effort into the net, sending the Hatters to Wembley for the final.
Stockport County: Hinchliffe, Lewis (Collar 61’), Horsfall, Hussey, Knoyle, Wright (Hippolyte 67’), Camps (Sarcevic 62’), Lemonheigh-Evans (Croasdale 61’), Rydel, Olaofe (Stretton 90+4’), Madden
Unused substitutes: Byrne, Jaros
Salford City: Cairns, Shephard, Vassell, Mariappa, Touray, Watt, Mallan, Bolton (McLoughlin 120+3’), Hendry (Lund 69’), McAleny (Barry 69’), Smith (Morton 105’)
Unused substitutes: Galbraith, Leak, Torrance
