Former Magpies midfielder Matt Gill put the Grecians ahead in the first half, before County skipper Michael Johnson levelled with a header after the break.
Two minutes into injury time Canham grabbed a point with a close-range header against his hometown club.
Exeter started brightly and Dean Moxey and Liam Sercombe both tested the goalkeeper in the early stages.
The Grecians deservedly took the lead midway through the half when Moxey's fine cross from the left was headed home powerfully at the far post by Gill.
Marcus Stewart broke well down the right for the Grecians and when he picked out Sercombe, the youngster's shot was charged down by Myles Weston.
Matt Hamshaw had a shot saved by Paul Jones following a rare raid by the Magpies, but Exeter were never threatened before half-time.
The Magpies looked far brighter after the break. Weston and Richard Butcher both forced Jones to make early saves as the visitors hunted an equaliser.
Jones again saved well to deny Jamie Forrester's close-range strike and Johnson headed Hamshaw's corner just past the post.
The equaliser came just before the hour mark when Hawshaw curled in a free-kick which was powerfully headed home by Johnson.
At the other end Russell Hoult saved well to deny both Ryan Harley and Richard Logan.
With three minutes left Harley's cross was flicked on by Logan and Taylor was in the right place to volley home at close range.
Two minutes into injury time Hamshaw burst into the box and when his shot was parried by Jones, Canham headed home from close in.