Barnet lost top spot in the National League after drawing at Eastleigh.
Tyrese Shade put the hosts ahead after 16 minutes, tucking away his fifth goal of season from Richard Brindley's cross.
Barnet went close to equalising before the break as home goalkeeper Joe McDonnell made an excellent diving stop from Anthony Hartigan's free-kick.
The Bees continued to press and Ryan Glover headed Ben Coker's corner onto the roof of the net.
The visitors were finally rewarded after 71 minutes when Glover crossed and Callum Stead flicked home, but wins for York and Forest Green dropped them to third.
Report supplied by PA Media
