Barnet fielded an unchanged side from the one that beat Yeovil in midweek.
They were without half a dozen of their squad players and were up against a strong City team, managed by the former Liverpool star Mark Wright.
The game opened brightly for Chester who were playing down the Barnet slope. Ryan Sugden had a 15-yard shot blocked by keeper Lee Harrison and moments later man of the match Kevin McIntyre had a left-footed drive intercepted by Harrison at the edge of the box.
For Barnet, Mark Gower had a shot on goal but Lee Woodyatt turned it for a corner.
After 33 mins, Barnet suffered a further injury blow when the former Arsenal player David Hillier was injured and he was replaced by Ishmail Yakabu.
In the second half, Leon Bell the Barnet midfielder was sent off for an over the top tackle on McIntyre.
This opened the way for Chester to push forward and it was no surprise when a Twiss cross was met by David Cameron and keeper Harrison could only get a foot to the ball to give Sugden an open goal from ten yards.
Manager Peter Shreeves had to gamble at this stage, he brought on two substitutes and pushed players forward to get an equalizer.
Unfortunately for the Bees in the 87th minute Scott Guyett put through an excellent pass for Twiss to score.
In the 90th minute substitute Mark Beesley scored from five yards from McIntyre's pass