Bantams boss Stuart McCall had boasted that his side had conceded just one goal in open play in the previous 11 games, a claim which was further boosted by Bradford's four successive clean sheets coming into this game.
And Barnet began the afternoon chasing their first home win since October.
Promotion-chasing Bradford gave as good as they got in the opening exchanges, with Peter Thorne going close on two occasions, but they soon started to struggle as they failed to come to terms with the pace of Albert Adomah, the aerial threat of Paul Furlong, the industry of Neal Bishop and the craft of Nicky Deverdics.
The breakthrough came in the 25th minute when a Deverdics corner was only half-cleared.
Veteran centre-half Gary Breen - still upfield for the set-piece - picked up the loose ball on the edge of the area and slid a clever ball through to Adomah, who gleefully drilled home from 15 yards.
Seven minutes later, another Deverdics corner from the right caused more havoc. This time Furlong rose to meet it with a firm header that just cleared Evans' left post.
Four minutes before the break, John O'Flynn increased Barnet's lead from yet another set-piece. Matt Lockwood was the provider, this time from the left wing, as the former Cork City man glanced a superb header home from the deftly-flighted free-kick.
The visitors' second half fightback never really materialised, although Michael Boulding gave them some hope when he bundled in a deflected Thorne shot at the far post on 56 minutes.
But the goal merely stung the Bees back into action, and two minutes later Yannick Bolasie cheekily turned in Furlong's goalbound shot from close range.
Barnet sealed the points in emphatic fashion just after the hour.
This time it was Joe Devera's turn to impress as he cut inside from the left and dispatched a low drive past a despairing Evans for his first goal of the season.
The punch-drunk visitors ended the game happy to escape further embarrassment as Barnet missed a host of late chances to increase the rout.