The Cherries looked to be coasting to victory when they cruised into a 3-1 lead, but Lincoln hit back after 86 minutes with Lee Beevers heading in a free-kick from Stefan Oakes.
Lincoln, who were outplayed for much of the game, then bombarded the Bournemouth goal and snatched a point in the fifth minute of injury time when midfielder Lee Frecklington fired home from outside the box.
The hosts had earlier taken the lead when Dany N'Guessan headed a simple goal after 19 minutes. But Bournemouth hit back with a spectacular long-range shot from Mark Molesley which beat City keeper Bob Burch from 30 yards.
The Cherries looked in complete control in the second half and after Jake Thomson missed a good chance they went in front with a penalty following Beevers' foul on Danny Hollands.
Brett Pitman converted the penalty after 65 minutes and 11 minutes later the forward sent Burch the wrong way from the spot again after Beevers had conceded a second spot-kick with a push on Jason Pearce.