The big centre-half powered home a 79th minute header from a Brian Barry-Murphy corner after Lee Frecklington looked like he had given the visitors all three points at Gigg Lane.
The Imps midfielder thundered home a superb header with 14 minutes remaining to put John Schofield's side in front after Jamie Forrester's 16th goal of the season had cancelled out Andy Bishop's fifth minute opener.
But Fitzgerald's immediate impact ensured the Shakers salvaged a fifth consecutive draw as Lincoln slipped to fourth in the table.
Bury started brightly and Glynn Hurst was denied a fourth minute opener by Alan Marriott's smart stop at his near post.
But from the resulting corner, Bishop rose unmarked at the far post to head home his 17th goal of the season.
The home side were in the ascendancy but they received a warning on 17 minutes when Frecklington flashed a drive wide following a swift Lincoln counter-attack.
However, it was the Shakers who should have doubled their advantage four minutes later when Hurst picked out Richie Baker but he directed his header wide of the mark.
The young midfielder went close again seconds later as he burst into the penalty area but Marriott produced another good block.
And Bury were made to pay for their wastefulness eight minutes before the break when Forrester slid home to convert Paul Mayo's excellent low cross.
The visitors had the first chance of the second period when the lively Spencer Weir-Daley skipped past his marker before squaring for Frecklington to fire over on 57 minutes.
The Imps midfielder was on target though with 14 minutes left when he met Ryan Amoo's superb cross with a thumping header from the penalty spot.
But Fitzgerald struck three minutes later to hand the hosts a share of the spoils with his near-post header.
And Chris Casper's side could have taken all three points when first Marc Pugh's 88th minute cross struck the post and then Bishop's header shaved the crossbar as Lincoln were forced to hold on.