The Ammies will meet AFC Fylde next Saturday in the Vanarama National League Promotion Final.
They needed penalty kicks to get past Eastleigh, who recovered well from falling behind.
Free-scoring defender Carl Piergianni put the hosts ahead three minutes before half-time.
But the Spitfires have a man who knows where the back on the net is as well.
Top scorer Paul McCallum once again got on the scoresheet to level just before the hour mark.
Both sides had their chance but there was to be no way through - even in extra time.
So it went down to penalties and Eastleigh’s Chris Zabroski was the man to miss at the vital point and it is Salford who got to Wembley and are one game from promotion.