Danny Carlton's 44th-minute header was enough to separate the sides in what was an edgy game at Christie Park.
Carlton broke the deadlock with a goal out of the blue. David Perkins lobbed a cross into the area which was met by Carlton whose looping header curled over Danny Potter and into the bottom left hand corner of the Canvey goal.
Two minutes later the Shrimps should have made it 2-0 after good work from Carlton presented Stuart Barlow with a golden opportunity. The striker had space and time but saw his first attempt beaten away by Potter, who then reacted superbly to beat away a second effort from Barlow.
The second half saw the Shrimps again produce the best chances, but they could not beat Potter.
The Canvey stopper saved superbly from a 30-yard Gary Thompson drive on 76 minutes before reacting well again to cut out a dangerous Garry Hunter cross.
The Shrimps then came close again as the visitors piled bodies forward in the final stages.
Michael Twiss was the closest to making it 2-0 when he beat Potter to a long clearance but saw his header crawl agonisingly wide of the right hand post.
Twiss and substitute Wayne Curtis both had near misses in the final moments with headers that just beat the crossbar.
The visitors caused the Shrimps few problems but almost snatched a last-gasp equaliser.
Jeff Minton broke through from midfield and beat Chris Blackburn's challenge but thankfully for the Shrimps Steven Drench read the situation well and raced from his goal to tip away Minton's effort.
Apart from the late surge, Canvey enjoyed a brief period on top in the first half as striker Kezie Ibe looked sharp in and around the box.
On 17 minutes he carved out a great opening for himself but produced a weak final shot, before drilling the ball well over from distance after getting free of his marker.