For Dagenham, who currently occupy the play-off spot Shrewsbury are aiming for, a draw will be enough to secure their place and will mean Town miss out after looking likely play-off candidates for most of the season.
Part of their problem has been the inability to turn dominance into goals and draws into wins - and that was evident again against Lincoln, as the home side dominated a ragged untidy encounter which saw a number of good chances go begging.
Top-scorer Grant Holt spurned two first half opportunities when he looked certain to add to his 19-goal tally and such was Shrewsbury's control of the game, over an hour had been played before keeper Luke Daniels was called upon to make a save.
In the seventh minute centre-back Kelvin Langmead sent Holt clear of the Lincoln defence, but his tame shot was blocked by the legs of Imps goalkeeper Rob Burch - and on the quarter hour Holt's strike partner Nick Chadwick was also guilty of a glaring miss, when he headed a superb Steven Leslie centre wide from close range.
Holt was wasteful again in the 34th minute when Burch palmed away his shot with not a Lincoln defender to be seen - and after the break Shrewsbury continued to press, but Ben Davies, Leslie and Chadwick were all unable to find a breakthrough.
In the 65th minute Daniels tipped over a Geoff Horsfield drive as Lincoln - whose own play-off hopes were ended last week - mounted their first significant attack.
Despite a late Shrewsbury rally which saw substitute Dave Hibbert head just over, the visitors comfortably held out for a point, which left Shrewsbury needing all three when they travel to Dagenham next Saturday.