Substitute David Brown scored the only goal as Accrington claimed victory.
Stanley made a bright start as Gary Roberts was denied by goalkeeper Richard McKinney before Anthony Barry missed the target with a header.
Canvey worked their way into the game and Lee Boylan's fierce drive from the edge of the area was well saved by Accrington keeper Stuart Jones.
Boylan went close twice after half-time before Brown netted the winner with a powerful volley after 68 minutes.
Accrington Stanley: Jones, Williams, Welch (Cavanagh 69), Flynn, Richardson, Jagielka (Brown 63), Craney, Barry, Roberts, Mangan (Proctor 75), Mullin.
Subs Not Used: Alcock, O'Neill.
Goals: Brown 68.
Canvey Island: McKinney, Duffy, Chenery, Theobald, Bimson, Kennedy, Sedgemore, Minton (Gregory 85), Clarke (Keeling 74), Tait, Boylan.
Subs Not Used: Harrison, Sterling, Bunce.
Referee: R Fletcher (England).