The fantastic 3-3 draw means the National League Bees are still very much still in it.
Ollie Watkins' long-range strike gave Brentford the lead but Shaq Coulthirst had other ideas and scored twice inside three second-half minutes.
Neal Maupay made it 2-2 from the spot after a controversial penalty.
Sergi Canos then fired Brentford into the lead but there was to be one more big moment in a classic Cup tie.
Dan Sparkes' stunning free-kick made it 3-3 and means the teams will meet against next week at Griffin Park.
Darren Currie said he was proud of his team and thinks they deserved a second stab at the west London club.
Brian Barwick, Chairman of the Vanarama National League, said: “It was a privilege to be at The Hive tonight and witness first-hand a quite incredible FA Cup 4th round tie between Barnet and Brentford.
“The match had everything and Barnet did the National League proud - and some. They fought for every ball and produced a fantastic three goal haul in the second-half.
“It would have been hard on either side had lost to a late winner. A draw - and a replay seemed a fair result.
“Fittingly for two teams who share the same nickname everybody leaving the stadium was absolutely buzzing!”