Louis Dodds struck in the 12th minute and then again five minutes from time to ultimately secure a 2-1 victory for the Imps.
This came after Shrews skipper Ben Davies had levelled matters with a sweetly-struck free-kick with 14 minutes remaining.
But Lincoln just about deserved to win this often untidy encounter, leaving Shrewsbury to reflect on just one win in eight matches and rapidly diminishing chances of making the play-offs.
Having been involved in 13 deals during the transfer window that have seen six players arrive and seven leave, Shrews boss Gary Peters put his final two acquisitions, James Constable and goalkeeper Scott Bevan on the bench as the home side quickly sought to bounce back following a 4-2 reversal at Bradford City in midweek.
But those hopes were hit on 12 minutes when Dodds curled home a free-kick from 20 yards to give the visitors an early lead.
During a low-key and often frustrating first half for the Shrews, they were unable to find any spark to their forward play, although top scorer Dave Hibbert almost levelled on the half hour when he seized onto a under hit back-pass only to be crowded out after rounding keeper Andy Marriott.
After the break and despite having less possession, Lincoln created the better opportunities and both Dodds and Ben Wright wasted good chances to increase the lead.
It appeared they would rue those misses when in the 76th minute when Davies struck a curling free-kick from the edge of the box that beat Marriott all ends up to notch his fifth goal of the campaign.
Within a minute Jamie Forrester blasted over a good Lincoln chance to regain the lead, while at the other end Marriott had to go full stretch when clawing away a header from Guy Madjo.
The last word, however, went to Dodds and when Shrewsbury failed to clear a long throw, he was on hand to give Lincoln victory, happily smashing the ball home from ten yards.