The Gulls took the lead on 10 minutes when Clacton's Lee Barrett sliced Jamie Mathews' left wing cross into the top corner of his own net.
The hosts had the better chances for the rest of the first half, but fell further behind 5 minutes after the restart when Jay Curran squared a ball across goal for Kyle Asante to tap home.
Andre Foster had a fine game in goal for Canvey and made two outstanding saves as Clacton tried to reduce the arrears.
However, the night was rounded off perfectly for the travelling support in injury time when Canvey Island FC Academy player Mitchell Gilbey scored on his debut for the first team having come on as a substitute 5 minutes earlier.