The young Gers controlled proceedings throughout and opened up a two-goal advantage through efforts either side of the half-time interval from Thompson Ishaka and Findlay Curtis.
However, David McCallum's side were forced to dig deep when the Spiders pegged the Light Blues back, with Allen turning in a composed defensive display alongside his partner, Kristian Webster, at the heart of the defence to see out the win.
Speaking to RangersTV after the triumph, the teenager commented: "I thought we started the game quite poorly, but as we grew into the game we began to play good football.
"It was a different challenge in the second half because we had to defend more and almost hold on at the end. But at the end of the day it's job done and into the final.
"We had a lot of chances, but that's football. If you don't take your chances, then you need to defend at the other end and I thought we done that well.
"It's something that the lads have shown in the games that we've played, that we can dig in to the last minute.
"Even though games can be tough, and the last ten minutes today were tough, the lads showed great courage and desire to hold on to the win.
"I've played with Kristian for quite a few years now and he's brilliant to play with.
"We have a good partnership and it's something that we needed today because it was a tough game."
Allen has endured an injury-hit campaign for Gers B and only marked his return to the pitch after a lengthy lay-off last month.
And the 18-year-old defender admits it was a tough period to be sidelined as he knuckled down in the gym to accelerate his rehab.
Now back on the pitch, the Scotland Under-19 international believes he has benefitted from his spell away from the training pitch to work on various aspects of his game.
He added: "It's been a tough, tough year, but the last three or four weeks have been good.
"It's definitely difficult, but it's part of football nowadays. You see a lot of players getting injured and coming back, but you need to have that other side of the game where you come back and trust your ability.
"It allows you to take a step back from football because it can become routine when you're training every single day.
"But when you're injured, it affords you the time to look at other sides of the game, like working on your body.
"Mentally, too, it can be tough, but you need to keep at it and the rewards will show."