Full of energy and creativity the visitors absorbed what pressure Rochdale could muster and then broke consistently at pace to create a hatful of chances before running out 2-0 winners.
The in-form Rochdale started the brighter and were denied after just two minutes when midfielder David Perkins saw his deflected effort superbly saved by Bees' keeper Lee Harrison.
As the visitors got the measure of the lacklustre home side they began to create chances of their own and, after 25 minutes they opened the scoring. Adam Birchall broke down the left and produced a hard low cross that was comfortably converted by Barry Cogan.
Nine minutes later Cogan turned provider when, after Adam Rundle had been dispossessed, Cogan's cross was met by a diving header from the on-rushing Dean Sinclair.
In the latter stages of the half Barnet could have extended their lead, but twice home keeper Matthew Gilks did well to deny Birchall.
Though Rochdale boss Keith Hill made two changes at half time the story continued after the break with his side being cut open almost at will. And, in the early stages of the half, Liam Hatch missed when it seemed easier to score and Gilks produced another fine save to keep out Jason Puncheon.
Rochdale rallied midway through the second half with Perkins going close and substitute Danny Reet missing the target on two occasions, but they never really looked like breaking down a resolute Barnet rearguard.
Dale might have produced a grandstand finish but Harrison produced a great save to keep out Glenn Murray and from the resulting corner Ismail Yakubu hooked a Simon Ramsden header off the line.