City took an early lead but then the Cherries took control and appeared to be heading for a comfortable victory until their late collapse.
Lincoln broke the deadlock in the 19th minute when Dany N'Guessan sent a looping header over Bournemouth keeper David Button for his seventh goal of the season.
The home team should have doubled their lead five minutes later when on-loan striker Anthony Elding stole in unmarked at the near post but sent his first-time shot wide.
Lincoln then lost their way and Bournemouth went close in the 35th minute when Steve Fletcher set up Jake Thomson but the midfielder fired his shot straight at Lincoln keeper Rob Burch.
The Cherries got on level terms a minute later when Mark Molesley collected a loose ball outside the box and beat Burch with a right-foot shot which crept in at the near post.
An error by Burch handed another chance to Thomson early in the second half but, with an empty net in front of him, the winger fired narrowly over.
Lincoln were in trouble again when Lee Frecklington brought down Danny Hollands on the edge of the box. The free-kick was touched to Brett Pitman whose low effort brought an excellent save from the Lincoln keeper.
Two minutes later Lincoln went behind after Lee Beevers found Hollands just inside the box and Pitman sent the keeper the wrong way from the spot-kick.
Eleven minutes later Beevers was again at fault when he pushed Jason Pearce to give away a second penalty and Pitman repeated his trick of sending Burch the wrong way to put Bournemouth 3-1 ahead.
Lincoln became increasingly desperate but got back into the game in the 87th minute when Beevers' header was too powerful for Bournemouth keeper Button.
Just as the game looked to have slipped away from Lincoln they drew level in the fifth minute of stoppage time. Frecklington fired in a low shot from outside the box and Button was caught out at his near post handing Lincoln an unlikely point.