Boro' will meet Conference Premier side Cambridge United in the final on Sunday 23rd March after this afternoon's superb win in the "Battle of Hampshire".
Alex Pike's side are also the first team from outside non-league football's top flight to make the final since Grays Athletic and Hucknall Town met in 2005.
A packed Privett Park had to wait an extra 15 minutes for the start in the afternoon sunshine as neighbours Gosport and Havant & Waterlooville prepared to continue from Monday night's 1-1 first leg.
And it was a tentative and nervous opening from both sides who were regularly guilty of giving away possession.
After few early chances, Scott Beven was forced into the first save of the game - pushing a header from his own defender round the post.
Andy Forbes then curled a 20-yard free kick around Bevan's post but it was the Hawks who were enjoying the majority of the possession and went closest with Perry Ryan's 25-yard driving narrowly missing the target.
Josh Carmichael then skipped through the Havant defence before firing over and Ciardini then wasted a glorious chance for the visitors - shooting wide after finding himself one-on-one with Nathan Ashmore.
The all important breakthrough came at the end of the half. A Boro' free-kick on the edge of the area was cleared but Brett Poate's shot was deflected for a corner and Mike Gosney's hanging kick was met by Sills who rose above the defence to give Gosport the advantage.
With their noses in front, Boro' started the better of the two teams in the second half and within minutes Lee Molyneaux should have punished Hawks but the Boro' man blasted over from eight yards.
But on the hour it was two and Sills again beat his former Torquay United team mate Bevan with a header after drifting away from his marker.
With Gosport 3-1 up on aggregate, Alex Pike's side were immediately reduced to ten men when a rash kick by Poate on Perry Ryan saw him receiving a straight red card.
The Hawks now pushed forward in a bid to find a way back into the game but the ten-men dug in and an unusually poor Havant performance meant that Ashmore was not troubled.
As the game entered its final stages, Gosport began to run the clock down and soaked up everything the visitors could muster.
After a massive six minutes of injury time, the final whistle prompted a huge cheer and pitch invasion amongst the Boro' contingent of the 2,901 crowd.