Defeat for the hosts would have seen their opponents move to within four points of them with two games in hand.
But Canvey's victory - their first since January 2 - now gives them a good chance of moving clear of the relegation zone and up the table.
Although a bitterly cold near gale force wind made conditions difficult and good flowing football impossible that mattered little to Canvey as they took the three points.
Canvey started the game with the elements in their favour. A free-kick from Dwain Clarke on the right saw visiting keeper Phil Smith punch the ball away for Canvey's fourth corner of the afternoon after 13 minutes.
The first real chance came after 17 minutes when teenage striker Jason Hallett ran on to a through ball and fired in a shot that Smith turned wide on 17 minutes.
Two minutes later Canvey were awarded a free-kick 25 yards out following a foul on ex-Crawley man Allan Tait and the set-piece was fired just wide by Jeff Minton.
Good play by John Kennedy on the right allowed Minton to fire in a 35th minute shot which Smith turned wide with a flying save.
A Lee Blackburn shot straight into home stopper Danny Potter's arms relieved the pressure on the visitors seven minutes before half-time.
Having survived against the wind without too many problems Crawley must have fancied their chances as the second-half got underway.
Crawley earned their first corner four minutes after the break and, after Potter had punched out Sacha Opinel's set-piece, Steve Burton's shot was blocked.
But Canvey broke to force a corner themselves and, when the ball wasn't cleared, defender Sterling headed home Minton's cross off the post after 52 minutes.
From a Crawley corner on the left the ball fell to midfielder Paul Armstrong and his well-struck 20-yard effort was turned wide by Potter after 67 minutes.