After both sides had exchanged early off-target shots it was the visitors who opened the scoring after five minutes, Tim Sills firing home into the bottom corner.
However, on 16 minutes Canvey levelled as Lee Boylan's cross was turned home by Steve Burton for his first goal for the Gulls.
The Shots continued to put pressure on home keeper Danny Potter, who denied Jake Robinson and Nick Crittenden, while Nikki Bull collected from Boylan at the other end.
The busy Boylan tested Bull once again with a long-range strike but the keeper kept hold of the effort.
Canvey then fell behind for the second time when Robinson netted from close range after Potter had initially blocked an effort from Adrian Caceres.
After Boylan was off target Canvey levelled for a second time on the stroke of half-time when the same player scored from Chris Duffy's cross in a carbon copy of the first goal.
Just three minutes into the second half Aldershot were reduced to ten men as David Lee was sent off after a second bookable offence.
However, whilst Canvey looked hopeful with their man advantage the Shots continued to press with Sills heading wide.
Bull was called into action to deny Mario Noto and Neil Midgley while Caceres shot straight at Potter at the other end.
The keeper was also busy denying Robinson, while Midgley shot across the face of the goal at the opposite end as both sides looked desperately for the winner.
Substitute John Keeling forced Bull into a save low down, but Aldershot could have snatched the win on 77 minutes but for a quality save by Potter.
A long ball forward from Darren Barnard picked Robinson out perfectly and the young striker's shot on the volley forced a superb stop from the keeper.
The Gulls also ended with ten men as Ollie Berquez was dismissed right at the death.