Alex Pike brought fit again Steve Claridge back to the starting line-up to attempt to provide another FA Trophy upset at the expense of Town, three divisions higher than Boro'.
But unsurprisingly, Boro' found it a difficult afternoon against the Essex side with the visitors in control for much of the game.
After the opening few minutes when Gosport had looked capable of causing Iron problems, the match quickly settled into one where Boro' were very much on the defensive for much of the time.
With the Boro' midfield unable to impose itself, the defence found themselves under mounting pressure but Town were guilty of some awful misses and, once again, Nathan Ashmore had a great game between the posts to deny the visitors on several occasions.
The 'keeper was forced into superb saves twice in the first half to deny Town's Wright and Quinton but he was unable to do anything about the single goal of the game which came on 52 minutes.
The goal was a headed effort from Dean Wells after Wright's corner but Boro' will kick themselves as loose play in midfield had presented Town the opportunity from the corner.
With Braintree now in the driving seat, Gosport looked unable to come up with any new ideas. Pike replaced Adam Wilde with Dan Wooden and then with a little over ten minutes left he withdrew defender Gavin Jones and replaced him with striker Ross Langworthy.
It turned out to be Boro's best spell of the game. As they chased for an equaliser, James Ford went close when his punt forward was tipped away by McDonald as it threatened to drop under the bar but despite their best efforts, the home side could not find a way through the solid Town defence in the final moments.
