They hit the woodwork three times, but were then indebted to Paul Mayo for a dramatic goal-line clearance.
The point keeps them in the play-off zone but Rovers were looking for all three to boost their hopes of joining them.
They pressed earnestly in search of a goal but were let down by poor shooting and Lincoln's back four generally controlled the box.
Lincoln's shots which bounced off the posts came from Mayo, Scott Kerr and sub Lee Frecklington, but their closest chance really fell to Jamie Forrester. Their top scorer was put clear by an ill-judged back-pass from Rovers' Sammy Igo, but he stumbled as he cut into the box and a great chance ended.
A lively ball on a hard surface made accuracy difficult but Rovers should have gone ahead in the first half when Ricky Lambert fastened on to a long ball from centre-back Steve Elliott. He got well behind his shot but Paul Morgan threw himself down and blocked it.
Lambert was behind another good Rovers effort, knocking the ball down to his partner Richard Walker, whose shot was a shade too straight and was collected by keeper Alan Marriott, who had a commanding game.
A well-worked free-kick routine almost saw Lincoln in front when Mayo hammered a left-foot shot against the post from all of 30 yards.
Two wide players, Lincoln's Junior Mendes and Rovers' Lewis Holdane each brought a touch of excitement when they were on the ball, but neither had the final accuracy to put their side in control. Mendes went close at the end of one neat move when he rolled a shot a foot or so wide, while a handful of eager Holdane shots were all off target.