CHESTER City slumped to their third defeat of the season, when they lost 3-1 on the sloping Underhill pitch on Saturday.
The North Londoners, who had failed to convert an earlier penalty, took the lead three minutes from the break when Mark Gower linked well with Neil Midgley before rifling the ball home past the despairing dive of Wayne Brown.
City had chances to equalise, but Hill and Haarhoff were guilty of bad misses. However the visitors did get back on to level terms after 68 minutes, leading scorer Mark Beesley taking advantage of some poor tackling before slotting the equaliser home.
Barnet, who lost their Football League status at the end of last season, came back strongly.
Prompted by substitute John Doolan, who was formerly a junior with Everton, they restored their lead after 74 minutes.
The 30-year-old Scouser set Midgley free, Brown advanced and got a hand to the striker's effort but the pace of the ball took it over the line.
Chester's disappointing afternoon was compounded nine minutes from time, when midfielder Scott Ruscoe became the second City player to be sent off this season, the ex-Newtown player being dismissed for a second bookable offence.
Boosted by their numerical advantage, Barnet increased their lead three minutes from time, when Ben Stevens swept the ball home following some neat work by Midgley.
The defeat means that Chester drop down to 16th place in the Nationwide Conference table.
BARNET: Harrison, Goodhind, Heald, Arber, Gledhill (Sawyers, 61), Bell (Doolan, 69), Niven, Gower, Toms (Flynn 84), Stevens, Midgley. Subs not used: Naisbitt, Taylor.
CHESTER CITY: Brown, S Rose, M Rose, Spink (Woodyatt, 78), Lancaster, Porter, Hill (Wright, 84), Kerr, Haarhoff (Hopwood, 62), Ruscoe, Beesley. Subs not used: Roberts.
REFEREE: Mr L. Proben (Bridgwater). ATT: 1,197.