Ben Sedgemore's header levelled the scores in the 90th minute after Jeff Minton had pulled one back for Canvey two minutes earlier.
Goals from Tim Sills and Leroy Griffiths had given Aldershot what had looked like an easy win before Canvey's late revival.
Shots dominated early and were given a great chance to take the lead on the half hour when Joe Dolan brought down Ryan Williams in the Canvey box.
However, Williams' spot-kick was brilliantly saved by Richard McKinney who dived to his left to push the ball behind for a corner.
Sills and Griffiths also had great chances to put the Shots ahead but both directed headers narrowly wide of the post.
Canvey defended well under pressure but offered little up front leaving Nikki Bull untroubled in the Shots goal.
After the break Aldershot finally took the lead in the 52nd minute when Lewis Hamilton's cross was met by Sills in the area and he flicked the ball past McKinney.
The lead was doubled in the 75th minute when Williams' free-kick was headed home by Griffiths.
Canvey then gained possession and searched for an opening but had no real clear-cut chances until the dying moments of the game.
The Aldershot defence failed to clear an incisive pass by substitute Mario Noto and Minton wasted no time in latching on to the ball and coolly sliding it into the net to give Canvey hope.
Two minutes later Sedgemore's downwards header from a Minton corner sealed Canvey's comeback and ensured an equal share of the points.