Rovers started strongly and went close after seven minutes when Hugh McAuley's corner was headed just over by Adam Garner from close range.
Four minutes later the home side were denied by the woodwork when a cross from the right wing was punched by keeper Scott Tynan, but only as far as Andy Harris, whose superb attempted lob cracked against the crossbar before being cleared.
Barnet's first dangerous attempt came just after the half hour when Ben Strevens' header needed Dean Williams to be at his best to tip the ball over the bar.
Disaster struck for Rovers ten minutes into the second half.
Alan Lewer chose not to replace the injured Matt Gadsby at half-time and paid the price when Richard Graham left Gadsby in his wake before sending over a low cross which Strevens headed into the right hand corner.
Twelve minutes later it was Garner's turn to add to Rovers' misery. A long ball over the top should have been cleared first time by the Forest Green defender but he hesitated and Liam Hatch nipped in to lob the ball over Williams to secure the win.