The Beavers got off to a great start when they went in front after just 8 minutes when a dangerous ball into the box bounced beyond Shaun Jeffers but found Max Kretzschmar at the far post and he slotted his effort past Braintree `keeper Nathan McDonald.
The home side almost doubled their advantage in the 20th minute when some excellent work from Kretzschmar, who won the ball back and then fed Jeffers inside the box, but McDonald saved well.
Nine minutes later, Hampton `keeper Seny Dieng was brought into serious action for the first time when a good run from Jonathan Muleba saw him feed the ball to Reece Grant inside the box. His sliding effort, however, was saved well low to Dieng's left.
On 36 minutes, a left-footed effort from the home side`s Brendan Kiernan just outside the box curled wide and then just before half-time, the Beavers conceded an equaliser when Grant's towering header sailed beyond Dieng into the back of the net.
Both sides battled hard as the second half wore on but neither keeper was being seriously tested.
But on 69 minutes there was a great chance for Braintree after Hampton failed to clear their lines when the ball fell to Josh Hill, whose drilled effort fizzed just wide of the post.
The Beavers had another scare 10 minutes from time when Dieng lost possession of the ball just outside his box. However, he redeemed himself by collecting the ball after a cross came in from the right.
However, a cagey second half sees the scores level after a well fought contest, so the final goes to extra-time.
Four minutes into overtime, The Iron had a great chance when a cross from the right found Grant, whose guided header flew just wide.
Three minutes later, the home side almost went ahead when sub Elliott Charles` cross fell to Kiernan in the six-yard box. However, he couldn't quite get a proper shot away and McDonald pounced on the ball.
Chances though were few and far between as the first period of extra-time ends and a penalty shoot-out looms.
The second extra 15 minutes was just as cagey as the prize at the end of the game seemed to be affecting the players, who don`t want to make a mistake that could cost them promotion.
So, it`s the lottery of a penalty shoot-out to decide, after 42 league games and three play-off matches, who will take their place in non-League football`s top competition next season.
Shaun Jeffers took the opening spot-kick for Hampton and converted, with Reece Grant skying his shot over the bar.
Josh Casey`s effort was saved by McDonald, Dan Thompson converted his shot, Elliott Charles stepped up next and scores, Marcel Barrington was next up for the Iron and converted with ease.
Brendan Kiernan was next for the Beavers and shot over the bar.
Josh Hill makes it 3-2 to the visitors Bradley Hudson-Odoi equalises at 3-3.
Diaz Wright wins the shoot-out for Braintree by beating Seny Dieng to make it 4-3 and it`s the Iron who go up.