The home side made the early running, but the visitors capitalised against the run of play. Johnny Hunt crossed for Kane Richards to stab the Blues into a 20th-minute lead.
Mikael Mandron missed two good chances to score for the hosts, which proved a turning point.
The Blues extended their advantage, despite a heroic penalty save by goalkeeper Scott Brown from Tom Shaw. In the ensuing scramble, Elliott Durrell poked in.
In their strenuous efforts to fight back, Eastleigh inadvertently gave Jordan Chapell the freedom of Ten Acres to race clear on the break and make it three.
Report supplied by the Press Association.
Match ends, Eastleigh 0, Chester FC 3.
Second Half ends, Eastleigh 0, Chester FC 3.
Goal!  Eastleigh 0, Chester FC 3. Jordan Chapell (Chester FC).
Substitution, Chester FC. Jordan Chapell replaces Kane Richards.
Goal!  Eastleigh 0, Chester FC 2. Elliott Durrell (Chester FC).
Substitution, Eastleigh. Alefe Santos replaces Ross Stearn.
Substitution, Eastleigh. Jamie Cureton replaces Scott Wilson.
Second Half begins Eastleigh 0, Chester FC 1.
First Half ends, Eastleigh 0, Chester FC 1.
Reda Johnson (Eastleigh) is shown the yellow card.
Goal!  Eastleigh 0, Chester FC 1. Kane Richards (Chester FC).
First Half begins.
Lineups are announced and players are warming up.
Eastleigh suffered a promotion setback with a demoralising home loss to Chester.