The Shrews squandered three golden first-half chances at the New Meadow and now head to Dagenham - their only rivals for the final play-off spot - knowing they must get three points to force their way into the top seven.
Leading goalscorer Grant Holt was the main culprit of the missed chances as he twice was played through by Steve Leslie but denied both times by the outstretched left leg of Imps' goalkeeper Rob Burch.
Nick Chadwick was just as culpable when he put a simple header wide from a Leslie cross, while Leslie's misplaced back-pass gave Geoff Horsfield a chance for the visitors but he shot weakly at Luke Daniels from only eight yards.
Lincoln, who had won their previous five games at Shrewsbury, nearly made it six with a header from Ben Wright and a free-kick by Stefan Oakes that Daniels scooped over.
And there was almost late drama at the other end when Holt was tripped in the penalty area in the fifth minute of injury time but Shrewsbury's desperate appeals for a penalty went unheeded.