The Bees scored an injury time winner through Ben Tompkins as they progressed to the third round of the FA Youth Cup.
An Okem Chime double cancelled out Joe Dearman and Richard-Noel strikes for the visitors but Tompkins rose highest in added time to seal a famous victory for Dan Senda's side.
The young Bees made the perfect start as Chime swept home George Murphy's cross to make sure he continued his streak of scoring in every round of the FA Youth Cup.
Moments later Chime was in again but on this occasion, the linesman raised his flag for offside, as the Bees looked to double their advantage in the opening 10 minutes.
Up the other end after 15 minutes the U's looked to respond, but Jake Battersby's effort sailed over the crossbar.
But almost immediately after the Bees had a golden chance to score a second of the evening, as Chime held the ball up well before slotting in Steven Bala who's shot was well saved by Louis Chadwick.
The next chance fell the way of Chime as he exchanged passes well before bending a shot that was again well stopped by the U's 'keeper.
As the half hour mark approached we almost saw a wonder-goal as Finlay Titchmarsh struck a sweet effort from 30 yards but it flew inches past the post and into the side netting. It would have been some strike from the young Bees midfielder.
The visitors levelled on 33 minutes as Joe Dearman slotted past Aymen Azaze to bring the U's back into the contest.
With five minutes to play before the break, Chime let fly from the edge of the box, but yet again his effort was palmed away by Chadwick, from the resulting attack Chime then saw an effort blocked away for a corner.
Into the second half and the visitors should have taken the lead as Thomas Dickens peeled away at the back post from a free-kick but couldn't quite make contact.
Up the other end, it was the Bees turn to miss guilt-edged chance as George Murphy fired wide when through on goal.
Azaze was called into action as he had to turn Simper's effort round the post afer the midfielder tried his luck from 25 yards out.
From the resulting corner kick, the visitors played a routine from the training ground only to see a powerful effort smash the upright and the follow-up sail harmlessly over the bar.
It was that Chime again minutes later! As the striker slotted home to give the Bees the lead once again, the striker who made his first-team debut on Sunday showing everyone why he's so highly rated at the Club.
But the lead didn't last long as the U's levelled again as Richard-Noel got himself on the scoresheet to make it two each in an entertaining cup tie.
The introduction of Wraynel Hercules gave the Bees pace on the break and he slotted in Murphy who looked to square it but he got his feet tangled and the chance went begging as the game approached the final 10 minutes.
As extra-time loomed the Bees found a dramatic late winner as Ben Tompkins flicked a header over the 'keeper and into the net to spark jubilant scenes on the touchline and a mass bundle in the corner!!
The Bees will now travel to the Vitality Stadium to take on AFC Bournemouth in the Third Round as a reward to their excellent run so far.
Barnet: Azaze, Fowler, Greco, Helcke(Kudrik '90 +3), Tompkins, Edwards, Titchmarsh, Bala (Granville '78), Chime, Murphy, Castillo (Hercules '64).
Unused Subs: Hamed, Fujah