National League South outfit Wealdstone, who won the non-League `double` in 1985 by beating Boston United at the `old` Wembley, had their hopes of making it through to the new home of English football dashed by the Northamptonshire side, who held a 1-0 lead from the first leg.
But Bobby Wilkinson’s side were unable to overturn that deficit in front of a season’s best attendance of more than 2,000 at Grosvenor Vale.
Wealdstone were indebted to keeper Jonathan North, who ensured the contest remained scoreless at the break with two fine saves to foil Aaron Williams as the visitors dominated.
But Brackley made the breakthrough 10 minutes after the break when Jake Sheppard brought down Glenn Walker on the edge of the area and Jack Byrne curled the resulting free-kick past North.
The Stones finally began to apply pressure in the second half, and Danny Green’s effort forced a save from Brackley keeper Danny Lewis, while skipper Jerome Okimo poked the ball wide from Sheppard’s free-kick.
But Williams put the outcome beyond doubt with 8 minutes to go when he slotted home a left-footed finish past North to clinch a 3-0 aggregate victory.
And Kevin Wilkin`s Brackley side will meet Neil Smith`s Bromley at Wembley.
Bromley were FA Amateur Cup winners back in 1910/11, 1937/38 and 1948/49, so have appeared at football`s headquarters before as a club, but made it through to the final of competition that effectively replaced the Amateur Cup for the first time on Saturday.
In front of a crowd of 2264 at the International Stadium, Gateshead, who trailed 3-2 from the first leg ay Hayes Lane, couldn`t have got off to a worst start as they went 4-2 down on aggregate after just 5 minutes when Brandon Hanlan surged through on goal and after his original shot was parried back towards him by the outstanding James Montgomery, the ball deflected back over the Heed number one off Fraser Kerr and into his own net.
Gateshead responded well to falling behind on the day though and a quickly taken free-kick was drilled into the box and headed goalwards by Richard Peniket, but Bromley `keeper David Gregory reacted well.
Frankie Raymond went close at the other end with a fine volley, but the half ended with the Ravens in command.
Shortly after the break, Wes York tucked a deep cross back across the face of goal for Danny Johnson, but the front man couldn't connect properly, and it went just wide.
Sutherland then made a terrific block to deny Russell Penn but in the 69th minute The Heed were back on level terms on the day when Scott Barrow scored with a thunderbolt from 25 yards that gave Gregory no chance.
However, Gateshead keeper Montgomery was called into action to make saves to deny Jordan Higgs at the far post, Louis Dennis with a wonderful one-handed save and then a remarkable save prevented Jordan Higgs from scoring.
Jordan Burrow had Gateshead`s final chance in the 89th minute, but he shot over from 20 yards and Bromley could celebrate a 4-3 aggregate victory.