City, who have now won just one of their opening eight league games, started well and threatened in the 13th minute when Dany N'Guessan got into a good position only to see his shot deflected wide.
Lincoln kept up the pressure and went close again four minutes later when N'Guessan was denied by a save from Barry Roche.
The ball fell to Adrian Patulea, but with the keeper stranded the Romanian striker saw his shot blocked by Danny Adams.
Lincoln went ahead after 20 minutes when midfielder Lee Frecklington ran through the Shrimps defence unchallenged, before finishing with a right-foot shot which left Roche helpless.
Diarmuid O'Carroll set up a chance for Craig Stanley as Morecambe got back into the game in the 26th minute, but the midfielder sent his shot straight at Lincoln keeper Rob Burch.
Lincoln defender Frank Sinclair then limped off with a knee injury and the game began to turn against the home team.
Morecambe had a great chance to level in the 43rd minute when Michael Twiss opened up the Lincoln defence, but Jim Bentley shot wide from six yards.
But Morecambe levelled in first-half stoppage time thanks to a fluke goal. Stanley fired a 50-yard free-kick into the box and the ball bounced through the crowded penalty area before finishing up in the back of the net.
Lincoln had the chance to go back in front on the hour when N'Guessan and Lenell John-Lewis set up Patulea, but the striker failed to get any power behind his shot and Bentley cleared off the line.
Morecambe finished well and went close in the 67th minute when Stewart Drummond won the ball in midfield and sent Twiss clear, but the winger's shot flew narrowly wide of the upright.
In stoppage time Burch saved Lincoln when he kept out a close-range header from Dave Artell as Morecambe threatened to get a winner.