The Bees - who ended the campaign in 11th but earned a play-off place when the season was concluded on unweighted points per game - will now travel to Notts County.
Darren Currie’s team shocked fourth placed Yeovil at Huish Park with a sensational second half showing.
It ended 2-0 in Somerset as the Londoners’ dug deep to win through.
After a timid first 45 minutes, reliable striker Paul McCullum broke the deadlock.
Eight minutes after half time he make jo mistake after Ephron Mason-Clark‘s pass.
The Glovers tried to work their way back into the tie but it was game over as they chased the leveller.
Mauro Vilhete made it safe with time running out and they will head to Meadow Lane next weekend looking to cause another big surprise.
The winner of that game will take on either Harrogate or Boreham Wood at Wembley.
"We rode our luck at times and it's nice to have that luck go our way a bit today," admitted Bees boss Currie, "but defensively, as a team, we worked hard.
"Our backline, goalkeeper and midfield worked tremendously hard, which was very pleasing. In some of our attacking play though, I've seen us play better than that.
"You don't win every game with pretty patterns and good football. Sometimes you have to roll your sleeves up and the boys did that today.
"We'll have to be mindful of how we prepare for the game (next week's semi-final with Notts County) because the boys will be tired, having played their first competitive match for four months.
"They'll be really excited by what they've done today and we'll all be looking forward to next Saturday".