The Imps, needing the points to stay in the race for the play-offs, got off to the best possible start.
Simon Yeo saw his curling cross come back off the far post but Francis Green headed in the rebound to give Lincoln a seventh minute lead.
Five minutes later the Shrewsbury defence was in trouble again, when Derek Asamoah took the ball off Trevor Challis and sent over a low cross, but Yeo was inches away from making contact.
Lincoln grabbed another goal in the 17th minute from a set piece move. Welsh Under-21 international Lee Beevers hurled in a long throw which Shrewsbury failed to clear and Yeo fired home his 21st goal of the season.
Lincoln then allowed Town back into the game but Mike Sheron shot wide after being set up by a great ball from Jamie Tolley.
Shrewsbury had another chance in the 25th minute when a mistake by Jamie McCombe let in Kelvin Langmead, but the striker's low shot was well saved by Alan Marriott.
At the other end Green, spurred on by his first goal in nine games, was denied by a diving save from Scott Howie.
Lincoln suffered a blow in the 55th minute when Yeo, back helping out his defence, went down with a knee injury and had to be stretched off.
Langmead twice went close for the Shrews, but Lincoln also wasted chances to extend their lead. Green produced a 69th minute cross which was headed back by Beevers only for midfielder Peter Gain to shoot wide from a good position.
Then Lincoln's teenage sub Oliver Ryan turned on the edge of the six-yard box, but hit his shot over the bar.
Shrewsbury's best chance came 16 minutes from the end when Andy Wilkinson burst through from defence, but his final shot was well saved by the diving Marriot.
A late error by Ryan Lowe gave Ryan a half chance, but Howie was quick off his line to save.