Michael Branch, Ryan Lowe and Tom Curtis all scored for Chester, who had Stuart Drummond sent off by referee Andy D'Urso in the 36th minute.
Barnet, who also finished the match with 10 men after Anthony Charles was sent off, grabbed a late consolation through Giuliano Grazioli.
Chester took the lead against the run of play when Michael Branch pounced in the 14th minute. The former Wolves striker bundled the ball over the line after Barnet failed to clear Ben Davies' short corner.
Until then Barnet had gone closest through Grazioli and Dean Sinclair who were both denied by Chester keeper Chris Mackenzie.
Barnet pressed for an equaliser with Grazioli, Damian Batt, Liam Hatch and Ben Strevens all spurning good chances .
Chester were then reduced to 10-men when Stuart Drummond was sent off for kicking out at Nicky Bailey. Referee Andy D'urso did not hesitate with his decision and produced a straight red card.
As the match swung in Barnet's favour Grazioli thought he had pulled the Bees level, but was unfortunate to see his scissor-kick from 12-yards strike the cross bar.
Chester then grabbed their second a minute before half time when Ryan Lowe latched on to Mackenzie's goal-kick before firing the ball into the bottom left corner.
After the restart Barnet looked to make their extra man count but they soon found themselves with only 10 men after Anthony Charles was shown a second yellow card for a late foul.
Their misery was added to when Tom Curtis scored Chester's third. The ex-Mansfield player was released by Lowe before producing a neat finish from the edge of the box.
Grazioli gave Barnet's fans some to cheer about when he scored from close range with 12 minutes remaining, but it was too late to spark a comeback.