The goal was harsh on the Imps after they had dominated throughout, but Bury caretaker boss Chris Casper will take anything at the moment, especially to enhance his claims of becoming the permanent successor to the departed Graham Barrow.
Keates gave the visitors the lead with a thunderbolt free-kick in the 43rd minute, but midfielder Whaley gave Bury a share of the spoils with a fierce drive which flew past Lincoln goalkeeper Simon Rayner into the bottom left-hand corner.
A scrappy first half was shaded by Lincoln who, after three minutes, could have taken the lead.
Gary Birch met a Scott Kerr cross from the right, but his glancing header was saved by Bury keeper Neil Edwards.
The visitors had another good chance in the 25th minute after a testing free-kick from Keates. His ball into the box eluded the Bury defence and was headed goalwards by Luke Foster, only for Edwards to make a brilliant point-blank save.
Bury's first chance of the half came five minutes before the interval. Midfielder David Buchanan saw a powerful left-footed shot deflected wide of the target.
A minute later centre-back Paul Scott headed into the side-netting from the resulting corner from Whaley.
But just when it looked as though it was going to be goalless at the break, Keates popped up with his stunning free-kick to give Lincoln the advantage.
It could have been 2-0 for Alexander's men if Marvin Robinson's goal on the stroke of half-time had not been ruled out for offside.
Lincoln started the brighter following the resumption and they were unlucky not go 2-0 ahead. Derek Asamoah found space on the edge of the six-yard box, but his clever shot on the turn hit the back post.
A minute later Robinson had another goal disallowed, again for offside.
It was not until the 56th minute when Bury had their first chance of the half. Whaley fired a shot wide of the target from the edge of the box.
Bury continued to press and defender Colin Woodthorpe saw a powerful shot well-saved by Rayner.
At the other end Tom Kennedy made a last-ditch block at the near post after a Birch had managed to sneak free and hit the target from close range.
The final passage of play was a scrappy one and neither side could conjure up a decent chance on goal, but Whaley was the hero with his splendid late strike.