Blues were a goal down within the first minute as Junior Baker passed back to Tony Tucker who took a heavy first touch, allowing Adam Wallace to score into the empty net.
Junior Baker had a header cleared off the line from a corner, and James Bunn also went close, with his header just going wide at the near post.
Enfield Town scored their second goal early in the second half as inspirational captain Mark Kirby headed home from a corner.
Joao Carlos was fouled inside the area with ten minutes remaining, and Harry Agombar scored from the spot to give the travelling faithful hope of a comeback.
Blues equalised with two minutes remaining as Junior Baker headed in from a Daniel Bunce corner to send the match into extra time.
With a number of Enfield players suffering through injury and cramp, Blues looked the more likely side to snatch the win, and had a number of consecutive corners in the second period, and Mark Kirby almost deflected a cross into his own net.
After 120 minutes, it came down to spot kicks, and it was the home side’s Noel Imber who was the hero saving from Joe Sweeney to send Town into Sunday’s play-off final.
They await the winners of the second semi-final between Tilbury and Needham Market, with that match due to take place on Friday at Chadfield. If the pitch is unplayable, they will try at Rookery Hill, and if that is also not passed fit, Tilbury will travel to Needham Market.