Town dominated from the start with Lincoln outplayed in all departments.
Shrewsbury went ahead after 28 minutes when the Lincoln defence failed to clear a cross from Kevin McIntyre and the ball came back in to the box allowing Jake Robinson to fire home.
Shrewsbury almost scored again two minutes later when Dave Hibbert got clear but failed to find the target with his shot.
Lincoln improved slightly following the second-half introduction of winger Jamie Clarke, whose pace caused problems for the Town defence. But Shrewsbury sealed their victory in the 76th minute when Lincoln defender Moses Swaibu handled inside the box and Hibbert sent the keeper the wrong way with the resulting penalty.
It could have been worse for Lincoln with Shrewsbury sub Lewis Neal missing two easy chances in stoppage time and Kris Bright shooting wide with the goal at his mercy.