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Full-time: Exeter City 2 Bury 2
BURY extended their unbeaten run to five games in all competitions but missed a raft of chances to claim victory.
Danny Nardiello put the visitors in front in the 15th minute with a low shot that seemed to go straight through Exeter keeper Artur Krysiak.
The Grecians stopper then atoned for his early blooper by clawing out a close-range Danny Hylton effort on the line.
Hylton broke clear on the half hour but pulled his shot wide and Exeter made Bury pay with a David Wheeler volley just before the break.
The Shakers edged back in front in the 47th minute with a powerful Nathan Cameron header from a Chris Sedgwick corner.
And, after Andy Procter saw a header tipped over, Tom Soares looked to have doubled Bury's advantage from the resulting corner.
His scrambled effort seemed to go over the line before being handled clear by Exeter midfielder Matt Grimes, but referee Stephen Martin ruled away claims for either a goal or penalty.
Exeter boss Paul Tisdale was roundly booed for his decision to replace Wheeler with young forward Tom Nichols.
But it proved a masterstroke as the youngster headed the home side back on level terms in the 77th minute.
Both sides then had chances to win it, with Nardiello for Bury and Nichols for Exeter missing the target with headers when they should have done better.
The failure to ram home their advantage saw Bury miss the chance to move up three places in League Two. They remain 20th in the table, two points above the drop zone.