The Bees looked on course for an eighth victory in nine matches, but a last-minute equaliser from AFC Telford's Michael Phenix earned the bottom club a share of the spoils.
At the bottom of the table, Alfreton won their first match of the season with a 2-0 triumph at Southport, and that success sees them move off the bottom of the standings.
Goals from James Mulley and Kenny Davis were enough for Braintree Town to condemn Kidderminster Harriers to a second defeat in four days, while Eastleigh remain in contention in the top half of the table after fighting back three times to earn a 3-3 draw at Altrincham.
A last-minute goal from Ellis Harrison helped Bristol Rovers move up to 12th place with a 3-2 win at Lincoln City, and the final result of the afternoon saw Nuneaton Town and Aldershot Town play out a 1-1 draw.
Results in full: AFC Telford United 2-2 Barnet, Altrincham 3-3 Eastleigh, Braintree Town 2-0 Kidderminster Harriers, Dover Athletic 0-1 Macclesfield Town, Forest Green Rovers 2-0 Halifax Town, Gateshead 1-0 Dartford, Grimsby Town 0-2 Torquay United, Lincoln City 2-3 Bristol Rovers, Nuneaton Town 1-1 Aldershot Town, Southport 0-2 Alfreton Town, Woking 1-0 Chester FC, Wrexham 2-1 Welling United