Lincoln went a goal down midway through the first half, but hit back to equalise and went close to a second-half winner.
Although Forest created plenty of chances, strikers Junior Agogo and Nathan Tyson looked out of sorts.
Forest began well and went in front with their first real attack after 24 minutes. Midfield Kris Commons picked out Agogo with a cross from the left and the striker saw his header half saved by Lincoln keeper Alan Marriott.
Forest claimed the ball had crossed the line, but Lewis McGugan ensured there was no doubt by blasting into the empty net.
Forest should have doubled their lead four minutes' later when Commons created another great chance for Agogo, but despite being unmarked inside the six-yard box, the striker sent his header against the bar.
Lincoln's equaliser came in the 38th minute out of the blue. Defender Paul Green sent over a seemingly harmless cross which was turned into his own net by Forest defender Kelvin Wilson.
That goal changed the game and inspired Lincoln. Ben Wright was unlucky with a downward header which bounced in front of goal and flew over the bar.
Then Dany N'Guessan was denied by an excellent save by Paul Smith.
Forest wasted another chance in the 64th minute when a defensive error let in Agogo but, with only the keeper to beat, he shot wide.
Lincoln's on-loan forward Louis Dodds was narrowly off target with a first-time effort three minutes' later.
But Forest's Commons smacked another late effort against the crossbar and Chris Cohen was denied in stoppage time by a point-blank save from Marriott.