A second-half penalty save by Bournemouth keeper Neil Moss proved the turning point as the Cherries grabbed their third away league win of the season.
Moss conceded the 61st minute spot-kick when he brought down Lincoln's Dene Cropper when the striker was clean through.
Moss was yellow carded but then dived to his right using his legs to block the powerfully struck penalty from Paul Smith.
Three minutes later the Cherries broke clear and took advantage of a mistake to fire home the winner.
A weak header from Mark Bailey failed to reach his keeper Alan Marriott and teenager Alan Connell nipped in to score an easy goal.
Bournemouth were unlucky not to add to their lead with substitute Steve Fletcher, back in action after a year out through injury, seeing a shot blocked on the line by Ben Futcher.
Twelve minutes from time Marriott produced a great save to keep out a shot from Wade Elliott. The rebound fell to Brian Stock but his rocket shot was blocked by City skipper Paul Morgan.
Earlier Bournemouth went in front with a 13th minute goal from defender Stephen Purches. The full back smashed home a shot from outside the box after the Lincoln defence failed to clear a corner.
Lincoln drew level four minutes later when Stuart Bimson floated over a free-kick. Futcher knocked the ball down and Cropper hooked his shot home from 15 yards.
Lincoln should have gone in front in the 20th minute when Smith's low cross found Simon Yeo but the striker completely missed his kick from ten yards out.
Yeo then saw a header loop onto the top of the bar before his frustration began to show. He produced a late tackle on Bournemouth defender Karl Broadhurst which earned a yellow card in first half stoppage time.
HASH(0x91be0ac)