After declaring publicly that Barnet were the team to watch with 14 games to go and little chance of promotion, Paul Fairclough's side were quick to oblige on Swindon's first visit to the Underhill Stadium.
In the sixth minute James Vincent unwisely conceded a free-kick 40 yards from goal.
Nicky Bailey lifted the ball into the box, Ismail Yakubu rose highest at the far post heading the ball into the six-yard box. Allen reacted quickest to squeeze the ball home and register his first goal for the club.
Still reeling, Swindon were nearly caught out again when Barry Cogan combined with Allen on the edge of the area but this time the player lacked his father's decisiveness.
Swindon's lack of guile and industry in the centre of the field belied their fourth place in League Two. Indeed the Robins became increasingly cagey as the half wore on and were only able to fashion one serious chance in the first half.
On 38 minutes Aaron Brown crossed from the left, Jerel Ifil climbed above the Bees defence but Rob Burch got down well to thwart the danger.
Swindon started the second half with far greater purpose. On 48 minutes Burch produced a stunning save from a powerful Christian Roberts header after the striker capitalised on a woeful clearance from Joe Devera. Unbeterbed the Bees continued to press and should have finished the game on 58 minutes.
Cogan left Andrew Nicholas for dead down the right when he crossed for Allen who was denied a certain goal following an amazing double block by Ifil. Swindon responded well, Simon King produced a Bobby Moore-esque tackle to thwart a run from Aaron Brown. Michael Timlin followed up and fired into the top corner, as he wheeled away to celebrate Burch produced a stunning save to deny the Fulham loanee.
As the game closed out Swindon looked more likely to score but lacked a striker which Paul Sturrock had desperately sought in the transfer window.