The Dons dominated possession for long periods of the game and were well worth their victory despite a late penalty miss by Chester.
The home side had actually started the brighter of the two teams and a well worked free-kick played to Tony Dinning saw the midfielder fire an early warning after three minutes, with his left-foot volley flying narrowly wide.
The Dons then exerted pressure on the home side, controlling the play and forcing several corners in quick succession which came to nothing. On 28 minutes Alan Navarro hit a great effort from outside the box which appeared destined for the bottom corner, until City captain Paul Butler got a timely deflection on the ball that sent it wide.
Ten minutes before the break Aaron Wilbraham had a great chance to put the visitors ahead when the ball broke to him inside the six-yard box, but his effort was smothered by keeper John Danby.
On 38 minutes the Dons deservedly took the lead when Wilbraham beat his man before squaring the ball to Mark Wright, who sidefooted home.
Chester showed more attacking intent in the early stages of the second half and wasted a good free-kick opportunity when Dinning rifled his shot straight at the defensive wall.
John Murphy came close to equalising for the Blues in the 58th minute when he latched on to a cross from Tony Grant, only for Willie Gueret to palm his effort around the post.
The league leaders doubled their advantage on 64 minutes after Lloyd Dyer left Simon Marples in his wake and crossed to Jemal Johnson, who arrived at the near post to poke the ball home via the woodwork.
Chester spurned a chance to get back into the game on 76 minutes with Wright adjudged to have handled the ball, sub Simon Yeo saw his penalty saved by Gueret.
Kevin Ellison and Yeo both had good opportunities in the final ten minutes, but could not find a way past the visiting keeper.