The Imps looked to have the game well in control when they led at half time but were denied a penalty shortly after the break which would have put the game beyond Shrewsbury. Instead referee Ray Olivier waved play on when Town defender Kelvin Langmead clearly handled a Lee Frecklington header inside the box.
Frecklington, being tracked by a number of Premiership and Championship clubs, went close in the second minute with a fierce shot from the edge of the box which was pushed wide by Scott Shearer.
But then a mistake by City's Nat Brown let in Michael Symes only for the striker to hit his shot straight at City keeper Alan Marriott.
Five minutes later Marriott made a mess of saving a 30-yard shot from Symes and was fortunate to see the ball pass straight through him and narrowly wide.
But Lincoln edged in front in the 17th minute when Lee Beevers whipped in a cross from the right which was headed in by Frecklington for his eighth goal of the season.
The goal simply inspired Shrewsbury to push forward even more and substitute Danny Hall, on for the injured Sagi Burton, was unlucky when his 19th minute header dropped on top of the bar.
Then Davies put a couple of long range efforts narrowly wide, but was unlucky three minutes before the break when his low shot was blocked by Marriott and then the follow-up from Dave Edwards was somehow kept out by the Lincoln defence.
Lincoln suffered a blow in first half stoppage time when their ex-Town striker Mark Stallard earned his fifth yellow card of the season for a late challenge on Richard Hope.
Lincoln's Northern Ireland international Jeff Hughes was close with a 56th minute shot but Town hit back quickly.
Davies pushed wide for the second half, got in an excellent cross in the 64th minute which Mike Jones headed home for the equaliser.