After a tight first period the Bees took the lead through Luke Gambin just 46 seconds after the restart.
Jake Hyde then did what he does best, twice, with two superb finishes to ensure all Bees left The Hive with a smile on their face.
The visitors, buoyed on by a loud travelling support, made the better start to the match but as the half wore on the Bees began to dominate.
There first chance came on 10 minutes as fantastic one touch football from Casabella and Yiadom pulled Chester apart before the latter found Keanu Marsh-Brown. He fired a cross into the box and Curtis Weston arrived at the perfect moment but he volleyed high and wide.
Two minutes later Elliot Johnson seized possession midway in the Chester half and let fly from 30-yards with his shot bouncing inches wide.
Birthday boy Marsh-Brown was outstanding throughout the half and Chester were unable to contain him, he had another chance with 22 minutes played but John Danby palmed the ball to safety.
Chester had a fair few set pieces but the Bees defended well and Graham Stack was rarely troubled.
With just 46 seconds played in the second-half Barnet took the lead through Gambin.
Byrne found Hyde whose shot was deflected into the path of Gambin, he moved one way then the other to create the space before slotting cooly into the corner.
With 59 minutes on the clock Chester had their best chance of the match as Paul Linwood's header was clawed off the line by Stack.
Four minutes later it was 2-0 as Jake Hyde tapped the ball home from five-yards after a great cross from Byrne and and even better initial pass from Roberto Casabella.
On 73 minutes it was game over as Luisma Villa surged into the Chester half and found Hyde who took one touch before lifting the ball over John Danby.
The visitors almost grabbed a consolation in the latter stages of the match but Stack saved before Andy Yiadom cleared the ball off the line.
Next up are two away matches against Tamworth and Gateshead where the Bees will be looking to kick on with another six points.
Barnet: Stack; Yiadom, Stephens, Saville, Johsnon; Casabella, Byrne, Weston; Marsh-Brown (Luisma 68), Gambin (Mengerink 77), Hyde (Crawford 83).
Barnet substitutes: Crawford, Vilhete, Luisma, Mengerink, Jupp.
Chester: Danby, Kay, McIntye Horan, Linwood, Harrison, Reed (Mills 60), Jarrett (N.Turner 68), Seddon, Lindfield, Mahon (Williams 83).
Chester substitutes: Fearon, Mills, Williams, N. Turner, L. Turner.