City looked confident in the opening 45 minutes but needed some excellent saves from keeper Alan Marriott to ensure they went in level at break.
Marriott did superbly in the 17th minute when Andy Cooke rounded Nat Brown and headed for goal. Marriott was quickly off his line and managed to block Cooke's shot with his legs.
But Lincoln could have sneaked in front in the 38th minute. Gary Croft sent the ball in from the left and new signing Steve Torpey saw his header clawed away by Town keeper Glyn Garner.
The second half was a different story as Lincoln were pushed aside by Town.
Marriott did well to save from Stewart Drummond and Cooke but was left helpless in the 52nd minute.
Darren Moss fired over a cross from the right which was completely missed by the City defenders. Cooke was then allowed to steal in unmarked at the far post and forced the ball home from close-range.
Lincoln were caught out again five minutes later when Dave Hibbert ran onto a ball over the top and easily beat the exposed Marriott.
Lincoln manager John Schofield responded by introducing ex-Town player Mark Stallard and Lincoln briefly got back into the game.
Stallard curled an effort narrowly wide in the 69th minute and then fired in another rare shot from Lincoln only for Garner to easily save.
Lincoln abandoned any thoughts of defence in the final 10 minutes in a desperate attempt to get a goal back but were caught out on the break.
Shrewsbury scored their third goal of the game in the 81st minute when Marc Pugh sent Cooke clear and the striker made no mistake from inside the box.
Just 60 seconds later Lincoln were caught out by another cross into the box. This time Shrewsbury sub Steve Leslie headed in.
It could have been even worse for Lincoln when Michael Symes beat Marriott with a last-minute effort but Gary Croft spared City's further embarrassment with a goal-line clearance.