Canvey started the first half well when they went ahead thanks to a sneaky header from Junior McDougald just outside the six-yard box.
Even though Exeter controlled most of the first half McDougald had another brilliant chance in the ninth minute when a well-weighted ball was played from the middle of the field, but Santos Gaia was in the way and his shot flew over.
Exeter's great passing was stopped by a much improved Canvey defence, who had suffered a recent string of home defeats.
The second half was just as exciting as the first and Exeter were putting on heavy pressure, but the Canvey defence held the one-goal margin up until Steve Flack's 71st minute goal.
Scott Hiley's cross was met by Flack's head and gave the Grecians a well earned equaliser.
After their leveller Canvey started to lose confidence and this led to Dominic Sterling's dramatic own goal as he headed the ball over his own keeper.
Then Canvey were behind for the first time in this game.
After a lot of effort from Exeter to gain the lead they lost it in the dying minutes when a Canvey corner was met by the head of David McGhee and his goal guaranteed a point for the home side, but they could have had three.