Frecklington burst forward before firing a low shot past Kasper Schmeichel from 20 yards. The 87th minute goal spared Lincoln the embarrassment of losing at home to the relegation-threatened Shakers.
Indeed City, despite being second best for most of the game, almost sneaked a late winner. Martin Gritton sent in a stoppage time shot which had Schmeichel beaten, but defender Colin Woodthorpe saved the day for with a goal-line clearance.
A victory for Lincoln would have been rough on Bury who did enough to have taken all three points.
The Shakers went close after just 15 minutes when a mistake by Lincoln central defender Jamie McCombe presented John Daly with a chance, but the striker shot over from the edge of the box.
Then Marc Pugh broke down the right flank but just failed to pick out Tom Youngs with his deep cross.
Lincoln hit back in the 19th minute when Scott Kerr sent in a shot from outside the box which Schmeichel managed to scramble away.
But Bury created the better chances and went close again in the 32nd minute and Daly rose above the Lincoln defence to meet a free-kick from Brian Barry-Murphy that headed wide from six yards.
Bury took the lead in the 37th minute when Daly set up Pugh, who beat a defender before shooting home from 10 yards.
Schmeichel made a point-blank save to keep out a shot from Jeff Hughes three minutes before the break as Lincoln became increasingly frustrated at their inability to create chances and the game looked to be slipping away from them.
Bury defender Chris Brass found Daly inside the box with a great pass but the striker sent his shot straight at Lincoln keeper Alan Marriott.
Then a 71st minute mistake by City's Gareth McAuley let in substitute Colin Marrison but the striker overran the ball and failed to get in the shot.
Bury should have wrapped the game up seven minutes from the end when Dwayne Mattis found himself in the clear. But the striker's shot brought an excellent save from City's skipper for the day Marriott making his 300th appearance for the Imps.