Man of the match Whaley struck a sensational equaliser from 30 yards that flew past keeper Kevin Miller into the top corner.
Until Whaley's goal Rovers were heading for their first away win in the League since last August. Instead, they had to settle for a club record 18th draw.
Craig Disley, back in the team after illness, put them in front against the run of play on the half hour.
Miller had made one final save to deny Dwayne Mattis while James Hunt was fortunate only to receive a yellow card for his tackle on Lee Unsworth.
With Bury in command Disley took advantage of a defensive lapse as the hosts failed to clear a free-kick and netted his fourth of the season from 10 yards.
Bury were far more dangerous in the second period and created a series of chances. Miller dived at the feet of Porter and also kept out another effort from the tall forward.
Mattis and Jon Newby also had efforts that just missed the target until Whaley found his range with a venomous shot.