Goals from Doug Loft and Ben Williamson gave Vale a 2-0 advantage before Jordan Clarke and Wilson's 90th-minute leveller secured a point.
In a frantic opening, Vale took the lead after just 37 seconds when a long clearance from goalkeeper Chris Neal evaded everybody and Valiants skipper Loft pounced to lob the ball over the oncoming Joe Murphy to slot into an empty net.
The second goal came after 73 minutes when Dickinson's cross was poorly cleared by the City defence allowing Williamson to head the ball in from two yards out for his fifth goal this season.
But after 81 minutes the Sky Blues got back into the game when substitute Mark Marshall's free-kick from the right was headed in by Clarke.
And a fantastic solo effort from Wilson - his fourth goal in four games - after 90 minutes completed the comeback to move the Sky Blues five points away from the drop-zone.