Town had striker Richard Walker sent off after only three minutes following an off-the-ball incident which left Lincoln defender Daniel Hone clutching his face.
But the Shrews reorganised with midfielder Chris Humphrey pushed forward to play alongside Grant Holt.
The pair combined in the 15th minute with Holt putting Humphrey away. The Lincoln defenders backed off but Humphrey's powerful shot brought a superb one-handed save out of Lincoln keeper Rob Burch.
Lincoln had plenty of possession but were restricted to long-range shots with Lee Frecklington twice sending an effort which failed to trouble Shrewsbury new keeper Matt Gilks.
Lincoln created a great chance in the 26th minute when Aaron Brown sent in an excellent cross from the left but Lenell John-Lewis was just unable to get the vital touch.
Lincoln always looked vulnerable to the counter-attack and an awful mistake by Daniel Hone let in the experienced Holt, but the home side were saved by a vital interception from Lee Beevers.
Nine minutes before the break, Lincoln's shaky defence looked suspect again when Kevin McIntyre fired over a corner.
Graham Coughlan was left unmarked but with a free header could not find the target.
Then a McIntyre free-kick deflected of a Lincoln defender and almost crept in.
Lincoln showed more attacking spirit in the second half and Gilks fumbled a long-range effort from Stefan Oakes but no Lincoln player was on hand to take advantage.
It was one-way traffic in the last half hour, but for all their effort Lincoln could not find a way through.
Beevers smashed a shot into the side-netting and then Gilks saved Frecklington.
Lincoln should have scored nine minutes from the end after Scott Kerr split open the Shrewsbury defence with an excellent pass.
But sub David Graham had two shots charged down and then an effort from Ben Wright was blocked.
Wright went close again when his low shot saw Gilks make another excellent save.