In the early stages the visitors' high energy approach caused a strangely lethargic looking home side problems and they were good value for the lead given to them in the second minute by Adam Birchall.
He reacted first as a long free-kick dropped in the box and he lashed a left-footed volley into the net from a tight angle.
Barnet should have doubled their lead on the half-hour when the home side failed to clear and the ball invitingly fell for Joe Tabiri, but from just 12 yards with the goal at his mercy he scuffed horribly wide.
The equaliser for the home side arrived on 37 minutes when, following a throw near the corner flag, the ball bounced off striker Chris Dagnall into the path of winger Adam Rundle who lashed it home with his right foot from a tight angle.
The home side got their noses in front just a minute before the break when skipper Gary Jones foraged for the ball which then sat up nicely for Dagnall, who simply rifled it into the net from the edge of the penalty area.
The second half was totally one-sided with the home team producing a series of flowing moves and they and striker Jon Shaw who was impressive throughout got his just rewards on 71 minutes.
A wonderfully struck pass from keeper Sam Russell that covered some 70 yards landed in the path of this run and the striker lashed it beyond keeper Rob Beckwith as he somewhat surprisingly opted to stay on his line.
Beckwith kept the scoreline down with two excellent saves to deny home substitute Adam Le Fondre as the home side looked to stretch their lead, but having seen his side concede ten goals in the first seven days of the season. Barnet manager Paul Fairclough will be looking for immediate improvement if they are to avoid a long hard winter.