A cracking golden goal from defender Darren Moss put Shrewsbury into the third round of the LDV Vans trophy.
Moss lashed home a 20-yard shot just four minutes into extra time which gave Lincoln keeper Paul Pettinger no chance.
The goal settled a fairly lifeless tie which sparked only briefly late in the first half. Lincoln went in front in the 39th minute when Adam Buckley smashed home a free-kick from the edge of the box after referee Phil Prosser moved the ball ten yards forward for encroachment.
Six minutes later, Shrewsbury drew level with an almost identical goal.
City's Tyrone Thompson was yellow carded for moving too soon at a Nigel Jemson free-kick. Again the ball was moved forward towards the edge of the box. After Jemson's second attempt was charged down, Luke Rodgers netted