The hosts led 2-0 entering the latter stages of the first period, but two quick-fire goals saw Stevenage level the scores entering the interval.
David Wheeler popped up with his second of the match late on, which seemed to be enough to claim all the points, but Whelpdale's brilliant strike levelled the scores in the 92nd minute as the two teams shared the spoils in a six-goal thriller.
The first chance of the match arrived inside the opening 60 seconds, but after finding space just inside the box, Clinton Morrison could only fire wide.
The hosts were ahead three minutes later, however, when Lee Holmes's dangerous cross was headed in by Wheeler. Stevenage came close in the 11th minute when Tom Conlon advanced into the penalty area, but his effort was wide of the post.
Exeter were 2-0 ahead after 15 minutes when Morrison scored an over-head kick to open his account for the club.
A topsy-turvy first half then produced a fourth goal and it was Stevenage that levelled the scores when Ben Kennedy rose highest inside the box to drop his header into the bottom corner.
An open start to the second period brought chances for both teams, but it was Wheeler that missed the best opportunity in the 55th minute when he could not direct Morrison's cross past Chris Day.
An end-to-end half continued to entertain, with Wheeler coming close on a couple of occasions for the hosts, while Armand Gnanduillet threatened for Stevenage as the game approached its final 15 minutes.
It took a wonderful strike from Wheeler to send the home team ahead, with the 25-year-old finding the bottom corner with a effort from a wide angle.
Stevenage almost levelled in the 83rd minute when Conlon curled an excellent free kick towards the top corner, but the ball rattled the crossbar. The visitors were not to be denied, however, as Whelpdale equalised with almost the last kick of the game.
The result has left Exeter 11th in the table, while Stevenage sit 20th, two points outside of the bottom three.