Whalley had been on the pitch 19 minutes when he fired a left foot set-piece through a crowded box into the bottom corner.
It had looked as if the visitors would leave east Lancashire with all three points after Richard Walker had headed his side into the lead on 58 minutes.
But it all went wrong in the dying stages as captain Stuart Campbell was also shown a red card for what looked like a push on Whalley.
In all fairness to Stanley though, who are now three points above the drop zone, they weren't the inferior side. In fact, for most of it they were actually the better of the two sides.
Both clubs came into the game on runs of four fixtures without a win and it certainly showed in a forgettable first half.
Neither outfit seemed capable of creating any sustained periods of pressure in the attacking third.
The hosts started the better and with a bit more purpose. Rommy Boco and Andy Todd had some early success down the flanks, while Andy Mangan looked lively upfront.
And it brought them the first real chance of the game when Mangan cut inside from the right to fire a low shot that bounced awkwardly in front of Steve Phillips in the Pirates goal.
Even though Paul Trollope's side were not really in the game, they should have actually taken the lead when Rickie Lambert blazed a volley over from the edge of the six-yard box after strike partner Walker had flicked on at the near post.
The second period started exactly the same as the first, with Stanley looking the more likely.
However, on 58 minutes, they were hit with the ultimate sucker punch. Central midfielder Craig Disley picked the ball up on the right wing to hook an inch-perfect ball on to the head of Walker, who did the rest with a powerful finish into the bottom right corner.
But then the late drama started as Whalley smashed home to send the paltry 1,300 crowd wild with delight.